Practice Questions for Business Statistics

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Chapter: Descriptive Statistics

Contents:

21-1 Questions (a) to (c) refer to the following figure:

40-2 Numerator

41-1 Denominator

46-4 which of the following two events is the more unusual

50-1 In what sense is the mean

715-1 Which are the correct real limits for the frequency table given below?

717-1 What can be said about these two classes?

723-1 A large mass of data can best be summarized pictorially by

1014-1 "For a symmetric distribution, the mean and median are"

1016-1 The mean and median for this data are:

1021-1 "increases 3 points, the median will become"

1403-1 "Find S**2, the sample variance."

1562-1 If you are told a population has a mean of 25 and a variance of 0

1719-1 Only a very small (5 or 10) percentage of measurements can

1743-1 ____X___________Frequency of X

1743-2 "If the mean, median and mode of a distribution are 5, 6, 7 "

1745-1 would be most influenced by an extreme score?

1745-3 the median as 65. One would expect this distribution to be

1746-1 sensitive to extreme scores on the higher or lower end

1746-3 Which of the following is not a measure of central tendency

1797-2 "In a group of 12 scores, the largest score is increased by 36 points."

1799-2 The quantity SUM(X - XBAR) is not used as a measure of dispersion

1802-3 "In popular usage, the term average may refer to:"

1803-1 The mean is a measure of:

1805-2 X(I)______Freq(I)

1810-1 The mean XBAR of the data above is

1811-1 A sample of 5 persons with hypertension underwent a special blood

1820-3 If a teacher computes the mean for a set of test scores and then

1821-1 "In a set of 10 scores the value 2 occurs three times, the value 4"

1838-1 Prepare the frequency distribution table

1839-2 whose hot dogs would you buy? Why?

1840-1 For each characteristic obtain a frequency plot

1847-2 Which worker appears to be faster in completing the job?

1849-1 Should the manager order the study repeated to

1855-4 Is this evidence that there is likely to be a mistake

1862-1 "3,3,3,3,3 is:"

1862-2 The sample variance of the following sample of five numbers

1864-1 "The variance, S(Y)**2, of the numbers 4, 6 is"

1866-1 Let us define a new statistic as the distance between 70th sample

1867-1 Which one of the following CANNOT be used as a measure of dispersion?

1874-1 "Generally, a small standard deviation implies that the measurements"

1876-1 Which of the following relations is always correct:

1878-1 "If a constant were to be added to a set of scores, the standard"

1878-2 Increasing the frequencies in the tails of a distribution will:

1879-1 "If the variance of a distribution is 9, the standard deviation is:"

1879-2 "If 5 were subtracted from each score, the standard deviation"

1879-3 What is the relationship between the variance of a set of scores and the

1883-1 Then which of the following statements about this second sample

1884-3 "Two suppliers offer a machine part with the required 1"" diameter."

1885-3 Which of the following indices will be changed from

1886-1 "Each year, during a period of seven years, Mrs. Smith gave birth "

1887-4 "Given that n = 25, SUM(i = 1,25)((X(i) - XBAR)**2) = 600, and"

1888-2 What is the standard deviation for the following set of scores:

1889-2 Calculate the variance and standard deviataion for the data given:

1891-3 Which data set has the larger standard deviation?

1896-3 The standard deviation of a group of scores is 0 when all the scores

1897-2 The standard deviation is a point in a distribution.

1899-1 The standard deviation is a measure of dispersion around the mean.

1901-2 "If the standard deviation of a set of scores is zero, "

1907-3 "[SUM(i = 1,n)(X(i)**2)]/n is:"

1910-1 "Find S**2, the unbiased estimator"

1911-1 "The variance, S**2, of this data is closest to:"

1914-1 "The variance for the sample [47.1, 33.1, 26.1, 40.1, 54.1] is:"

1916-1 The variance of a group of 10 scores was 16. If 2 were subtracted

1920-1 The scores that have the greatest effect on the value of the variance

1920-3 Why is the numerator squared?

1950-1 The variance of a set of negative numbers is negative.

2000-1 would you expect the histogram for the group to look most like

2002-1 Explain why histograms and frequency polygons are used in statistics.

2003-1 Construct a histogram using the 9 class intervals.

2005-1 "Using your relative frequency histogram, indicate "

2006-3 Plot a histogram showing roughly the relative frequencies

2008-1 Construct a frequency distribution using the class limits:

2009-3 Explain why the above graph is misleading.

2011-1 Assume half the subjects are male and half are female.

2012-1 Discuss the problems involved in drawing a histogram from this table.

2014-1 HISTOGRAM

2015-1 "In Table A, what proportion of those whose reading speed was more than"

2016-1 and a relative frequency diagram are drawn for the following data:

2017-1 a person with a raw score of 10 has a higher score than what percent

2019-1 the total number of cases observed at each score value

2019-3 the width of each interval would be:

2020-1 "If the same test were administered to fifth graders, what"

2020-2 A frequency distribution provides the following information:

2030-1 Relative frequency distributions permit comparisons between

2033-2 A percentile score of 40 indicates that a person

2033-3 If a person earned a score higher than 35 persons in his class

2034-1 is approximately equivalent to a percentile rank of ________?

2036-1 "Using the above distribution, answer the following questions."

2037-1 "Complete this sentence: ""The kth percentile of a given distribution"

2038-1 the 78th percentile. If five points were added

2038-2 If a given score is at the 30th percentile for reference group

2042-2 "If 40% of a group obtain scores below 70, the percentile rank of"

2043-2 Half (50%) of the values in a distribution are

2044-1 "On the same test, Tom scored at the 87th percentile, and Bill scored"

2045-1 For items (i)-(iii) use the following graph.

2050-4 Explain to a friend who has not studied statistics what this fact

2053-3 The 40th percentile of a distribution is the value above which

2053-4 "If the percentile rank for the value 60 is 40, this means that"

2057-4 Frequency distributions are useful for ALL BUT which of the following

2065-1 The skewness of the population is:

2066-1 How may the distribution be described?

2119-2 A graphical presentation may accomplish ALL BUT which of the following

2890-3 A sample is:

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Questions:

21-1

    Q:  Questions (a) to (c) refer to the following figure:

                   |
                   |
        Frequency  |              B
                   |
                   |           B     B
                   |
                   |              A        C
                   |                    C     C
                   |
                   |         A         A
                   |               C               C
                   |          B        B
                   |      A   C           A             C
                   |   A   C B          B    A             C
                   |A C   B                 B   A               C
                   --------------------------------------------------->
                                          Score

                   NOTE:  Connect the A points with a smooth curve to form
                          distribution A, the B points with a smooth curve
                          to form distribution B,  and the C points with a
                          smooth curve to form distribution C.

        a.  In the figure, which distribution's mean differs from the mean
            of the other two distributions?

        b.  In the figure, which distribution has the smallest standard
            deviation?

        c.  In the figure, is it likely that the mean of distribution A
            corresponds closely with the mode of distribution B?

            a.  Yes            b.  No            c.  Cannot be determined

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40-2

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.
        Numerator

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41-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.
        Denominator

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46-4

    Q:  Explain briefly how you would decide which of the following two events
        is the more unusual:

        a.  A 90 degree day in Vermont.
        b.  A 100 degree day in Florida.

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50-1

    Q:  In what sense is the mean of any distribution the "best guess"
        of the score of any single individual selected at random from
        the group?

        a.  In a series of such guesses, the sum of the errors in one
            direction will balance the sum of the errors in the other
            direction.

        b.  The mean score will occur more often than any other single
            score.

        c.  The chances are 50-50 that any individual will be above or
            below the mean.

        d.  All the above are true.

        e.  None of the above is true.

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715-1

    Q:  The heights of a sample of ten people are:

             67  73  70  60  67  66  68  71  70  67.

        Which are the correct real limits for the frequency table given below?

             Frequency        (a)         (b)         (c)

                 1         60.5-63.5     60-62     59.5-62.5
                 0         63.5-66.5     63-65     62.5-65.5
                 5         66.5-69.5     66-68     65.5-68.5
                 3         69.5-72.5     69-71     68.5-71.5
                 1         72.5-75.5     72-74     71.5-74.5

             (1)  Column a is correct
             (2)  Column b is correct
             (3)  Column c is correct
             (4)  All of columns a,b,c are correct
             (5)  None of columns a,b,c are correct

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717-1

    Q:  Ms. Sweetwater's biology class had a standard deviation of 2.4 on a
        standardized test, while Ms. Quincy's biology had a standard deviation
        of 1.2 on the same test.  What can be said about these two classes?
            a.  Ms. Sweetwater's class is more homogeneous than Ms. Quincy's.
            b.  Ms. Quincy's class is less heterogeneous than Ms. Sweetwater's.
            c.  Ms. Quincy's class did less well on the test than Ms. Sweet-
                water's.
            d.  Ms. Sweetwater's class performed twice as well on the test as
                Ms. Quincy's.

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723-1

    Q:  A large mass of data can best be summarized pictorially by means
        of:

        a.  the range
        b.  a histogram
        c.  the frequency table
        d.  XBAR and S(Y**2)

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1014-1

    Q:  For a symmetric distribution, the mean and median are
          1.  the same
          2.  always different
          3.  possibly the same, possibly different
          4.  insufficient information.

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1016-1

    Q:  Consider the following data:
             1, 7, 3, 3, 6, 4

        The mean and median for this data are:

        A. 4 and 3           D. 4.8 and 3
        B. 4.8 and 3 1/2     E. 4 and 3 1/2
        C. 4 and 3 1/3

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1021-1

    Q:  A distribution of 6 scores has a median of 21. If the highest score
        increases 3 points, the median will become  ___________.

             a.  21
             b.  21.5
             c.  24
             d.  Cannot be determined without additional information.
             e.  none of these

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1403-1

    Q:  Consider the following data:

                53, 61, 38, 65, 72, 58, 52, 63, 69, 74, 66

        You are given that SUM(i = 1, 11)(Y(i) - YBAR)**2 = 1082
        and SUM(i = 1, 11)(Y(i)) = 671.

        i)   Find YBAR, the sample mean.

             a)  67.1    b)  98.4    c)  108.2    d)  61.0
             e)  None of the above

        ii)  Find S**2, the sample variance.

             a)  98 4/11      b)  108.2      c)  0      d)  67.1
             e)  None of the above

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1562-1

    Q:  If you are told a population has a mean of 25 and a variance of 0,
        what must you conclude?

        a.  Someone has made a mistake.
        b.  There is only one element in the population.
        c.  There are no elements in the population.
        d.  All the elements in the population are 25.
        e.  None of the above.

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1719-1

    Q:  True or False?  If False, correct it.

        Only a very small (5 or 10) percentage of measurements can be more
        than two standard deviations from the mean.

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1743-1

    Q:  The sample mean of the following sample

                  X           Frequency of X
             -----------------------------------
                  2                 1
                  3                 2
                  4                 3

        is:    (1)  3
               (2)  2
               (3)  20
               (4)  20/9 = 2.22
               (5)  20/6 = 3.33

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1743-2

    Q:  If the mean, median and mode of a distribution are 5, 6, 7 respec-
        tively, then the distribution is:

        1.  skewed negatively
        2.  not skewed
        3.  skewed positively
        4.  symmetrical
        5.  bimodal.

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1745-1

    Q:  Which of the following measures of central tendency tends to
        be most influenced by an extreme score?

        a. median
        b. mode
        c. mean

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1745-3

    Q:  In a frequency distribution of 250 scores, the mean is reported as 78
        and the median as 65.  One would expect this distribution to be

        a.  positively skewed.
        b.  negatively skewed.
        c.  symmetrical but not rectangular or normal.
        d.  normal.
        e.  rectangular.

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1746-1

    Q:  The measure of central tendency which is sensitive to extreme scores
        on the higher or lower end of a distribution is the:

        a.  median.
        b.  mean.
        c.  mode.
        d.  all of the above
        e.  none of the above

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1746-3

    Q:  Which of the following is not a measure of central tendency?

             a.  mean               d.  standard deviation
             b.  median             e.  none of these
             c.  mode

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1797-2

    Q:  In a group of 12 scores, the largest score is increased by 36 points.
        What effect will this have on the mean of the scores?
            a.  it will be increased by 12 points
            b.  it will remain unchanged
            c.  it will be increased by 3 points
            d.  it will increase by 36 points
            e.  there is no way of knowing exactly how many points the mean
                will be increased.

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1799-2

    Q:  The quantity SUM(X - XBAR) is not used as a measure of dispersion
        because it is:

        (a)  always equal to zero
        (b)  always a positive value
        (c)  too difficult to work with
        (d)  always a negative value.

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1802-3

    Q:  In popular usage, the term average may refer to:

             a.  The mean
             b.  The median
             c.  The mode
             d.  None of these
             e.  All of these

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1803-1

    Q:  The mean is a measure of:

        a.  variability.
        b.  position.
        c.  skewness.
        d.  central tendency.
        e.  symmetry.

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1805-2

    Q:  The mean of the following data is:

             X(I)      Freq(I)
            ----------------
               0         4
               1         3
               2         1
               3         0
               4         1

        a.  9/5
        b.  9
        c.  9/4
        d.  1
        e.  none of the above

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1810-1

    Q:  Consider the following data:

             -4, 3, 8, -2, 7, 7, 6, 11, 4, 10

        The mean XBAR of the data above is

        (a)  4.00          (d)  5.60
        (b)  4.60          (e)  none of these.
        (c)  5.00

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1811-1

    Q:  A sample of 5 persons with hypertension underwent a special blood-
        pressure-reducing treatment program which resulted in the following
        reductions in systolic blood pressure for these persons (i.e. the
        scores give SBP after treatment - SBP before treatment): -5, 10,
        20, 5, 10.  The mean of this sample is

        a.  10      b.  9      c.  8      d.  40      e.  none of these

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1820-3

    Q:  If a teacher computes the mean for a set  of  test  scores  and  then
        subtracts  this mean from each score, the SUM of the resulting set of
        difference scores will equal

        a.  zero.
        b.  unity.
        c.  n, the number of scores.
        d.  the mean.
        e.  n times the mean.

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1821-1

    Q:  In  a  set  of  10 scores the value 2 occurs three times, the value 4
        occurs twice, 6 occurs twice, and 7 occurs three times.  What is  the
        mean of the scores?

        a.  (2 + 2 + 6 + 7)/4
        b.  (2 + 4 + 6 + 7)/10
        c.  (3*2 + 2*4 + 2*6 + 3*7)/4
        d.  (3*2 + 2*4 + 2*6 + 3*7)/10

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1838-1

    Q:  The following data represent scores of  50  students  in  a  calculus
        test.

             72    72    93    70    59    78    74    65    73    80
             57    67    72    57    83    76    74    56    68    67
             74    76    79    72    61    72    73    76    67    49
             71    53    67    65   100    83    69    61    72    68
             65    51    75    68    75    66    77    61    64    74

             a.  Prepare the frequency distribution table and the frequency
                 histogram for this data set.

             b.  Compute the sample mean XBAR, sample median X(M), sample range
                 R, interquantile range  and sample variance S**2.

             c.  Does the data set represent a sample or a population?
                 If it is a sample, describe the population from which it
                 has been drawn.

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1839-2

    Q:  a.  For each of the samples listed below obtain:
            1.  a mean
            2.  a variance, and
            3.  a standard deviation

            Each sample was randomly obtained from the production of the hot
            dog manufacturer listed.

                   Company               Dog Length(inches)

                     A                    5,5,5,5,5
                     B                    6,5,5,5,4
                     C                    9,9,5,1,1
                     D                    9,5,5,5,1
                     E                    9,5,5,5,5,5,5,5,5,1
                     F                    9,9,9,4,4,3,3,3,3,3

        b.  Given that the price per hot dog is the same for all manufacturers,
            whose hot dogs would you buy?  Why?

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1840-1

    Q:  Below are measurements of characteristics for two samples of interest,
        For each characteristic obtain:

            a.  Mean
            b.  Variance
            c.  Standard deviation
            d.  Frequency plot
            DATA:

                   MALE HEIGHTS (inches)               LENGTH OF INDEX FINGER (inches)
               66       71                            3.0       3.2
               68       71                            3.5       2.8
               69       72                            3.4       2.9
               68       69                            3.5       3.1
               71       71                            3.7       3.1
               73       70                            3.2       3.3
               67       72                            3.5       3.2
               68       69                            3.4       3.5
               65       70                            3.1       2.9
               72       70                            3.5       3.1

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1847-2

    Q:  Two workers on the same job show the following results over a long
        period of time.

                                                   Worker       Worker
                                                      A            B
        -------------------------------------------------------------------
        Mean time of completing the job (minutes)    30           25
        Standard deviation (minutes)                  6            4

        a.  Which worker appears to be more consistent in the time he
            requires to complete the job?  Explain.

        b.  Which worker appears to be faster in completing the job?
            Explain.

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1849-1

    Q:  Suppose the manager of a plant is concerned with the total
        number of man-hours lost due to accidents for the past 12
        months.  The company statistician has reported the mean number
        of man-hours lost per month but did not keep a record of the
        total sum.  Should the manager order the study repeated to
        obtain the desired information?  Explain your answer clearly.

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1855-4

    Q:  Answer the question by circling either "YES" or "NO" and by responding
        to the subsequent question if it applies to your answer.

        Suppose I calculate the mean of a distribution to be 15 and the stan-
        dard deviation to be 15.  Is this evidence that there is likely to be
        a mistake in my calculations?

        YES or NO?  If YES, why?

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1862-1

    Q:  The sample variance of the following sample of five numbers
        3,3,3,3,3 is:

             (1)  0
             (2)  3
             (3)  9
             (4)  11.25
             (5)  45

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1862-2

    Q:  The sample variance of the following sample of five numbers
        1,2,3,4,5 is:

             (1)  2.5
             (2)  9
             (3)  10
             (4)  13.3
             (5)  55

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1864-1

    Q:  The variance, S(Y)**2, of the numbers 4, 6 is

        (a)  2.0
        (b)  1.0
        (c)  0.5
        (d)  0.25

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1866-1

    Q:  Let us define a new statistic as the distance between 70th sample
        percentile and 30th sample percentile.  This new statistic would give
        us information concerning

        a.  central tendency.
        b.  variability.
        c.  relative position.
        d.  skewness.
        e.  symmetry.

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1867-1

    Q:  Which one of the following CANNOT be used as a measure of dispersion?

        a.  The difference between the third and first quartiles
        b.  [SUM(X(i)-XBAR)]/[n]
        c.  [SUM(]X(i)-XBAR])]/[n]
        d.  The difference between the 90th and 10th percentiles

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1874-1

    Q:  True or False?  If False, explain why.

        Generally, a small standard deviation implies that the measurements
        are clustered close to the mean.

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1876-1

    Q:  Which of the following relations is always correct:

        1.  SUM(X) = 0
        2.  SUM(X - XBAR) = 0
        3.  SUM(]X - XBAR]) = 0
        4.  SUM((X - XBAR)**2) = 0
        5.  SUM(X - a) = 0

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1878-1

    Q:  If a constant were to be added to a set of scores, the standard
        deviation would:

        a.  remain the same.
        b.  increase by the square root of that constant.
        c.  increase by the square of that constant.
        d.  increase by the magnitude of that constant.
        e.  none of the above.

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1878-2

    Q:  Increasing the frequencies in the tails of a distribution will:

        a.  reduce the standard deviation.
        b.  not affect the standard deviation.
        c.  increase the standard deviation.
        d.  not affect the standard deviation as long as the increases are
            balanced on each side of the mean.
        e.  none of the above

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1879-1

    Q:  If the variance of a distribution is 9, the standard deviation is:

        a.  3
        b.  6
        c.  9
        d.  81
        e.  impossible to determine without knowing n.

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1879-2

    Q:  The standard deviation of a group of scores is 10.  If 5 were
        subtracted from each score, the standard deviation of the new
        scores would be
          1.  2
          2.  10/25
          3.  5
          4.  none of these.

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1879-3

    Q:  What is the relationship between the variance of a set of scores and the
        standard deviation of those scores?
            a.  variance = (standard deviation)**2
            b.  standard deviation = (variance)**2
            c.  variance = mean/standard deviation
            d.  standard deviation = mean/variance

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1883-1

    Q:  A sample of 5 persons with hypertension underwent a special blood-
        pressure-reducing treatment program which resulted in the following
        values giving reduction in systolic blood pressure for these per-
        sons (i.e. the scores give SBP after treatment - SBP before treat-
        ment):  -5, 10, 20, 5, 10.

        Suppose for a second sample of 5 persons, the sample mean is 10, and
        the sample variance is 25.  Then which of the following statements
        about this second sample is not correct?

        a.  A person with a SBP reduction of 20 units is 2 standard deviations
            above the sample mean.

        b.  A person with a SBP reduction of -5 units is 3 standard deviations
            below the sample mean.

        c.  The sum of the squared deviations of SBP reduction scores from
            the sample mean, i.e. SUM((X - XBAR)**2), is 100.

        d.  The sample median cannot be determined from the information pro-
            vided.

        e.  Any SBP reduction score between 0 and 20 is within one standard
            deviation of the sample mean.

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1884-3

    Q:  Two suppliers offer a machine part with  the  required  1"  diameter.
        Samples  indicate  that supplier A's product has a standard deviation
        of 0.12 in. and supplier B's product has a standard deviation of 0.15
        in.  Which of the following statements is true?

           a. A offers a more homogeneous product.
           b. B offers a more homogeneous product.
           c. The standard deviation has no relationship  to the quality of the
              product.
           d. Only the mean is important in buying the machine part.

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1885-3

    Q:  The following set of scores is obtained on a test, X:  4,  6,  8,  9,
        11,  13,  16,  24,  24,  24,  26.   The  teacher  computes all of the
        descriptive indices of central  tendency  and  variability  on  these
        data,  then  discovers that an error was made, and one of the 24's is
        actually a 17.  Which of the following indices will be  changed  from
        the original computation?

        a.  Median
        b.  Mode
        c.  Range
        d.  Standard deviation
        e.  None of the above

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1886-1

    Q:  Each year, during a period of seven years, Mrs. Smith gave birth to a
        child.  The standard deviation of the ages (in whole years) of the 7
        children of the family Smith is equal to
        a.  2
        b.  4
        c.  7
        d.  Cannot be calculated if the present age of the children is not known

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1887-4

    Q:  Given that n = 25, SUM(i = 1,25)((X(i) - XBAR)**2) = 600, and
        XBAR = 156, calculate the variance and standard deviation.

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1888-2

    Q:  What is the standard deviation for the following set of scores:
        1,1,7,13,13?  In calculating the standard deviation, use the
        formula below:

        S = SQRT ((SUM(X-XBAR)**2)/(n-1))

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1889-2

    Q:  Calculate the variance and standard deviataion for the data given:

             (58, 50, 55, 53, 59)

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1891-3

    Q:  Listed below are two sample data sets, S and T.  Which data set
        has the larger standard deviation?  (Hint:  you can answer this
        question by inspecting the two data sets.  But if you are not
        sure after inspection, calculate the standard deviation.)

                Data Set S:  1, 2, 3, 4, 5, 6, 7, 8, 9
                Data Set T:  8, 9, 9, 9, 10, 11, 11, 12

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1896-3

    Q:  True or False?  If false, correct it.
        The standard deviation of a group of scores is 0 when all the scores
        are the same.

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1897-2

    Q:  True or False?  If False, correct it.

        The standard deviation is a point in a distribution.

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1899-1

    Q:  True or False?  If False, correct it.

        The standard deviation is a measure of dispersion around the mean.

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1901-2

    Q:  True or false?  If false, explain why.

        If the standard deviation of a set of scores is zero, all the
        scores have the same value.

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1907-3

    Q:  [SUM(i = 1,n)(X(i)**2)]/n is:

        a.  the variance.
        b.  the standard deviation.
        c.  the variance only when the mean equals zero.
        d.  the standard deviation only when the mean equals zero.
        e.  none of the above.

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1910-1

    Q:  Consider the following data:
                53, 61, 38, 65, 72, 58, 52, 63, 69, 74, 66.

        You are given that SUM(i = 1,11)([Y(i) - YBAR]**2) = 1082 and
        SUM(i = 1,11)(Y(i)) = 671.  Find S**2, the unbiased estimator
        of the sample variance.

        a)  98 + 4/11
        b)  108.2
        c)  61
        d)  67.2
        e)  none of the above

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1911-1

    Q:  Consider the following data:
           1,7,3,3,6,4

        The variance, S**2, of this data is closest to:

        A. 2    D. 5
        B. 3    E. 6
        C. 4

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1914-1

    Q:  The variance for the sample [47.1, 33.1, 26.1, 40.1, 54.1] is:

        a.   72.8               d.  122.5
        b.   98.0               e.  none of these
        c.  143.1

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1916-1

    Q:  The variance of a group of 10 scores was 16. If 2 were subtracted
        from each score, the variance of the new scores would be:

             a.  14
             b.  4
             c.  16
             d.  none of these

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1920-1

    Q:  The scores that have the greatest effect on the value of the variance
        are those

        a.  above the mean.
        b.  below the mean.
        c.  nearest the mean.
        d.  farthest from the mean.

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1920-3

    Q:  The sample variance is calculated as the average of the squared devia-
        tions of all the scores from the mean:
            SUM(i=1,n)([[X(i)-XBAR]**2]/[n-1]
        Why is the numerator squared?
        a.  Because otherwise you could get a negative variance, and this is
            not allowed.
        b.  Because otherwise the variance would always be equal to 0.
        c.  Because then the square root of the variance (i.e. the standard
            deviation) is in the original measurement units.
        d.  Because then the mean absolute deviation is minimal.

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1950-1

    Q:  True or False?  If false correct it.

        The variance of a set of negative numbers is negative.

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2000-1

    Q:  The median weight for a group of men is 65 kg;  the mean is 75 kg.
        Based on your knowledge of the mean and median would you expect
        the histogram for the group to look most like (a), (b), or (c)
        below?

        a)        |
                  |
        Frequency |            ---
                  |            | |
                  |            | |--
                  |            | | |
                  |          --| | |--
                  |          | | | | |
                  |          | | | | |--
                  |          | | | | | |
                  |        --| | | | | |
                  |        | | | | | | |
                  |        | | | | | | |--
                  |        | | | | | | | |
                  |        | | | | | | | |--------
                  |        | | | | | | | | | | | |
                  |        | | | | | | | | | | | |--------
                  |        | | | | | | | | | | | | | | | |
                  |        | | | | | | | | | | | | | | | |
                  --//-----------+--------------------------->
                  0                65
                                Weight in Kg


        b)        |
                  |
        Frequency |
                  |
                  |               ---
                  |               | |
                  |               | |
                  |             --| |--
                  |             | | | |
                  |           --| | | |--
                  |         --| | | | | |--
                  |         | | | | | | | |
                  |       --| | | | | | | |--
                  |       | | | | | | | | | |
                  |       | | | | | | | | | |
                  --//-----------+--------------------------->
                  0                65
                                Weight in Kg


        c)        |
                  |
        Frequency |
                  |
                  |                    ---
                  |                    | |
                  |                  --| |
                  |                  | | |
                  |                --| | |--
                  |                | | | | |
                  |              --| | | | |
                  |              | | | | | |
                  |              | | | | | |
                  |          ----| | | | | |
                  |          | | | | | | | |
                  |      ----| | | | | | | |
                  |      | | | | | | | | | |
                  |      | | | | | | | | | |
                  --//-----------+--------------------------->
                  0                65
                                Weight in Kg

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2002-1

    Q:  Explain why histograms and frequency polygons are used in statistics.

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2003-1

    Q:  On a final examination, the following scores were earned:  5,6,7,7,
        10,15,16,16,17,17,22,22,22,25,26,28,31,33,35,37,40.  Use these data to
        answer the following 4 questions.

        1.  Construct a frequency table for this data, grouping the data
            into 9 class intervals.

        2.  Construct a histogram using the 9 class intervals.  Be sure to
            properly construct and label the histogram.

        3.  What are the exact or real limits of the lowest class interval?

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2005-1

    Q:  Suppose that the variable Y can only take on the following five values
        with relative frequencies as indicated below:

            Y        Rel. Freq.        Cumulative Rel. Freq.
            -        ----------        ---------------------
            0            5/100
            1           25/100
            2           30/100
            3           25/100
            4           15/100

        a.  Fill in the cumulative relative frequencies.

        b.  Using 5 classes with unit widths and identifying the midpoints of
            the classes with the values of Y, plot the relative frequency
            histogram for the data.

        c.  Using your relative frequency histogram, indicate the positions
            of the mean, median, and mode.

        d.  If relative frequency is given as the interpretation of probability,
            then what is the probability that Y is greater than or equal to 2?

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2006-3

    Q:  A report states that a measurement is approximately normally
        distributed with mean 3.5 and variance 1.  Further, it states that
        measurements were recorded for 7 measurement classes 0-1,1-2, etc.
        Plot a histogram showing roughly the relative frequencies of these
        measurement classes.

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2008-1

    Q:  Given the following data:

                18, 13, 2, 20, 8, 10, 5, 10, 6, 9, 10, 20, 2
                15, 16, 16, 13, 10, 17, 10, 3, 2, 15, 8, 5

        a)  Construct a frequency distribution using the class limits:
            1-4, 5-8, 9-12, 13-16, 17-20.

        b)  Construct a relative frequency histogram using the results
            of part a).

        c)  Why might it be useful to construct a frequency distribution
            and/or a histogram of the sample data?

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2009-3

    Q:                |
                      |
                  150 +             -----
                      |             |   |
                  100 +     -----   |   |
         # OF         |     |   |   |   |
        PEOPLE     30 +     |   |   |   |   -----   -----
                      |     |   |   |   |   |   |   |   |
                    5 +     |   |   |   |   |   |   |   |   -----
                      |     |   |   |   |   |   |   |   |   |   |
                      --------+-------+-------+-------+-------+-----
                       1       2       3       4       5
                           or less                         or more
                                     AGE OF CAR IN YEARS

          Explain why the above graph is misleading.

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2011-1

    Q:  Suppose you are given a data set to analyze.  The data consist of 1000
        observations on one variable, the height of the subject being inter-
        viewed.  Assume half the subjects are male and half are female.  The
        sample mean height of the males is larger than the sample mean height
        of the females, while the sample standard deviation of the females is
        larger than the sample standard deviation of the males.  Both histo-
        grams are approximately symmetric.  Draw two histograms, one for males
        and one for females, to illustrate these facts.

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2012-1

    Q:  A friend of yours heard that you were taking statistics and has
        presented you with the following table from which he wants you to
        construct a histogram.

             Age      Relative Frequency (%)
            -----     ----------------------
             0-14              28.4
            15-44              50.5
             45+               21.1
                              -----
                              100.0

        Discuss the problems involved in drawing a histogram from this table.

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2014-1

    Q:  Define the following term and give an example of its use.
        Your example should not be one given in class or in a handout.

        HISTOGRAM

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2015-1

    Q:  TABLE A    The following table is a cross-tabulation of age and
                   reading speed of 100 pupils.

                                    Age to the nearest month

                      94-103  104-113  114-123  124-133  134-143  144-153 | f(Y)
                                                                          |
                 46-51           4        1                               |  5
        Score    40-45  2       10        5                               | 17
        on       34-39  1        5        2                               |  8
        reading  28-33  2        8        6        3        1        1    | 21
        speed    22-27           9       13        3                      | 25
                 16-21  1        5        4        2        1        1    | 14
                 10-15           2        3        3        1        1    | 10
                 ---------------------------------------------------------------
                 f(X)   6       43       34       11        3        3    |100

        In Table A, what proportion of those whose reading speed was more than
        33 were aged between 104 and 113 months?

        a.  19/30
        b.  27/51
        c.  19/43
        d.  27/43
        e.  19/100

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2016-1

    Q:  Both a frequency diagram and a relative frequency
        diagram are drawn for the following data:

                 X      f
                15      3
                17      5
                19      4
                23      3
                29      1

        We can state that
        a.  both will have the same values on the horizontal axis.
        b.  the frequency diagram will be less precise than the
            relative frequency diagram.
        c.  one depicts data in many-value classes while the
            other depicts single-value classes.
        d.  both depict continuous variables.

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2017-1

    Q:  The figure below indicates that a person with a raw score of 10 has a
        higher score than what percent of the persons in the group?

                        |           NOTE:  In order to complete the figure,
                        |                  connect the *'s with a smooth curve.
        Cumulative      |
        Proportion  100 +                               *
                        |
                     90 +                       *
                        |                   *
                     80 +
                        |
                     70 +
                        |
                     60 +
                        |
                     50 +
                        |
                     40 +               *
                        |
                     30 +
                        |
                     20 +
                        |           *
                     10 +       *
                        |  *
                        *---+---+---+---+---+---+---+---+-------->
                            2   4   6   8  10  12  14  16
                                      Raw Score

                        a.  10        b.  50        c.  82        d.  93

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2019-1

    Q:  A  list  of  the percentages of the total number of cases observed at
        each score value or each subinterval of scores is:

        a.  a histogram                             d.  a normal distribution
        b.  a relative frequency distribution       e.  none of these
        c.  a cumulative frequency polygon

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2019-3

    Q:  If  our  lowest score were 40, and the highest score were 189, n=200,
        and we decide to group our scores into 15 class intervals for a
        frequency distribution, the  width of each interval would be:

        a.  5
        b.  10
        c.  12
        d.  15
        e.  Insufficient information to answer

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2020-1

    Q:  A  reading  test  with  50  possible  points  yields  a   bell-shaped
        distribution  with  scores  ranging from 5 to 48 on a large sample of
        third graders.  If the same test were administered to fifth  graders,
        what would we expect the form of the frequency distribution to be?

        a.  Negatively skewed (skewed to the left)
        b.  Symmetric and bell-shaped
        c.  Symmetric, but not bell-shaped
        d.  Positively skewed (skewed to the right)
        e.  None of the above

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2020-2

    Q:  A frequency distribution provides the following information:

        a)  The value of the measurement and the number of individuals with
            that value.
        b)  The value of the measurement and the percent of individuals with
            that value.
        c)  The value of the measurement and the percent of individuals with
            that value or a smaller one.

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2030-1

    Q:  True or False?  If False, correct it.

        Relative frequency distributions permit comparisons between data sets
        of different sizes.

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2033-2

    Q:  A percentile score of 40 indicates that a person

        a. answered 40% of the questions correctly on the test;
        b. knows 40% of the material covered by the examination;
        c. has earned a score equal to or better than 40 persons in
           his class;
        d. has earned a score equal to or better than 40% of the
           persons in his class.

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2033-3

    Q:  If a person earned a score higher than 35 persons in his class
        of 50 students, what is his percentile score?

                a. 35
                b. 50
                c. 70
                d. 90

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2034-1

    Q:  The scores on a midterm examination are presented below in decreasing
        order of magnitude.  A score of 63 is approximately equivalent
        to a percentile rank of ________?
        65    63    61    60    57    56
        65    62    61    59    57    56
        65    62    60    59    57    56
        64    62    60    58    57    48
        64    61    60    58    57    47
        a.  20
        b.  25
        c.  63
        d.  80

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2036-1

    Q:       Class interval     f      Cum f     Cum %

                75-83           5       200      100.0
                66-74          12       195       97.5
                57-65          15       183       91.5
                48-56          38       168       84.0
                39-47          60       130       65.0
                30-38          40        90       35.0
                21-29          13        30       15.0
                12-20          10        17        8.5
                 3-11           7         7        3.5
                           -------
                             N=200

        Using the above distribution, answer the following questions.

        1)  The frequency of 38 in the interval 48-56 means:

             a.  38 frequencies are at the upper real limit of the interval.
             b.  38 frequencies are at the lower real limit of the interval.
             c.  38 frequencies are spread out throughout the interval.
             d.  38 frequencies are at the upper apparent limit of the
                 interval.
             e.  38 frequencies are at the lower apparent limit of the
                 interval.

        2)  A cumulative percentage of 97.5 means that:

         a.  97.5 cases fall below a score of 74.
             b.  97.5% of the cases fall below a score of 74.
             c.  97.5% of the cases fall below a score of 65.5.
             d.  97.5% of the cases fall below a midpoint of the interval
                 66-74.
             e.  97.5% of the cases fall below a score of 74.5.

        3)  The score above which 35% of the cases are found is:

             a.  70
             b.  40
             c.  38.5
             d.  29.5
             e.  47.5

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2037-1

    Q:  Complete this sentence: "The kth percentile of a given distribution
        is ...":

             a.  the score at which k% of the cases fall.
             b.  the score above which k% of the cases fall.
             c.  the score below which k% of the cases fall.
             d.  cannot answer without knowing the precise numerical
                 value of k.
             e.  more than one of the above is correct.

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2038-1

    Q:  Edith G. obtained a score of 65 in a statistics test, placing  her  at
        the  78th  percentile. If five points were added to each score in the
        distribution, her new score would be at the:

             a.  83rd percentile.
             b.  78th percentile.
             c.  70th percentile.
             d.  none of the above.
             e.  impossible to answer without additional information.

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2038-2

    Q:  If a given score is at the 30th percentile for reference group
        A and the 60th percentile for reference group B, which of the
        following is most likely true?

        a.  Individuals in reference group B generally performed
            better on the test than those in group A.

        b.  A person at the 15th percentile with group A will be
            at the 30th percentile with group B.

        c.  A person at the 80th percentile with reference group B
            will be at the 50th percentile with group A.

        d.  Individuals in reference group B generally scored lower
            on the test than those in reference group A.

        e.  None of the above.

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2042-2

    Q:  If 40% of a group obtain scores below 70, the percentile rank of
        the score is:

        1.  30        4.  70
        2.  40        5.  none of these
        3.  60

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2043-2

    Q:  The following data are the number of hours worked per week by seven
        State College students:

              3,      7,      4,      6,      2,      8,      19

        Half (50%) of the values in a distribution are

           a. included in the range          c. between the mean and mode
           b. between Q(1) and Q(3)          d. the mode and the highest value

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2044-1

    Q:  On the same test, Tom scored at the 87th percentile, and Bill scored
        at the 73rd.  This means

        a.  Tom is 14% better than Bill.
        b.  Tom scored 14 more points than Bill.
        c.  14% of those taking the test got scores ranging between Tom's
            and Bill's.
        d.  there were only 13 people smarter than both Tom and Bill.
        e.  none of the above.

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2045-1

    Q:  For items (i)-(iii) use the following graph.

                  Ogives of Distributions of Arithmetic Test
                    Scores for Seventh and Eighth Graders

              (Note:  Connect 7's with a smooth curve for seventh
               grade ogive and connect 8's with a smooth curve for
               eighth grade ogive.)

                100+------------------------------------------------7---------8
                   |        |         |         |         |         |         |
                   -        |         |         |         |     7   |       8 |
                   |        |         |         |         |         |         |
                 90+--------|---------|---------|---------|--7------|-----8---|
                   |        |         |         |         |         |         |
                   -        |         |         |         7         |         |
                   |        |         |         |         |         |         |
                 80+--------|---------|---------|-------7-|---------|---8-----|
                   |        |         |         |         |         |         |
                   -        |         |         |      7  |         |         |
                   |        |         |         |         |         |         |
                 70+--------|---------|---------|---------|---------|-8-------|
                   |        |         |         |         |         |         |
                   -        |         |         |         |         |         |
                   |        |         |         |         |         8         |
         PERCENT 60+--------|---------|---------|---------|---------|---------|
                   |        |         |         |         |         |         |
                   -        |         |         |         |         |         |
                   |        |         |         |         |         |         |
                 50+--------|---------|---------|---------|---------|---------|
                   |        |         |         |         |         |         |
                   -        |         |         7         |     8   |         |
                   |        |         |         |         |         |         |
                 40+--------|---------|---------|---------|---------|---------|
                   |        |         |         |         |         |         |
                   -        |         |         |         |         |         |
                   |        |         |         |         |         |         |
                 30+--------|---------|-----7---|---------|--8------|---------|
                   |        |         |         |         |         |         |
                   -        |         |         |         8         |         |
                   |        |         |         |         |         |         |
                 20+--------|---------|-7-------|-------8-|---------|---------|
                   |        |         |         |         |         |         |
                   -        |       7 |         |   8     |         |         |
                   |        |         |         |         |         |         |
                 10+--------|---------|-------8-|---------|---------|---------|
                   |        |         |         |         |         |         |
                   -        7         8         |         |         |         |
                   |        |         |         |         |         |         |
                  0+----7---|--8------|---------|---------|---------|---------|

                            5        10        15        20        25        30
                                           TEST SCORE

          (i)  What is the estimated percent of 8th grade pupils whose arith-
               metic scores fall below the median score for grade 7?

               a.   6
               b.  12
               c.  16
               d.  24
               e.  It is impossible to estimate this percent from the ogives.

         (ii)  What would be the shape of the frequency distribution corres-
               ponding to the 8th grade ogive?

               a.  Skewed to the left
               b.  Skewed to the right
               c.  Bimodal
               d.  Unimodal and symmetrical
               e.  It is impossible to tell from the ogive.

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2050-4

    Q:  Suppose that the 60th percentile of a sample was 1468.3.  Explain
        to a friend who has not studied statistics what this fact tells you
        about this sample.

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2053-3

    Q:  True or False?  If false, correct it.

        The 40th percentile of a distribution is the value above which
        60% of the distribution of values will fall.

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2053-4

    Q:  True or False?  If false, correct it.

        If the percentile rank for the value 60 is 40, this means that
        60% of the observations will fall above 40.

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2057-4

    Q:  Frequency distributions are useful for ALL BUT which of the following
        objectives?

        a)  Investigation of characteristics of each observation.
        b)  Summarization of data.
        c)  Condensation of large sets into smaller sets.
        d)  Illustration of the amount of variability in data.

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2065-1

    Q:  The mean of the population of ten scores, 78, 91, 91, 94, 74, 23, 63,
        22, 78, 89 is 70.3, and the modes are 78 and 91.  The skewness of the
        population is:

        1.  negative
        2.  zero
        3.  positive
        4.  not determined
        5.  positive or negative depending on the score.

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2066-1

    Q:  The distribution of entrance test scores of freshmen in a  particular
        university   has  the  following  percentile  scores.   How  may  the
        distribution be described?

                             Percentile           Score
                             ----------           -----
                                95th               140
                                80th               120
                                65th               101
                                50th                94
                                35th                91
                                20th                87
                                 5th                80

        a.  Symmetrical bell-shaped
        b.  Skewed left (negatively skewed)
        c.  Skewed right (positively skewed)
        d.  Impossible to tell from the above

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2119-2

    Q:  A graphical presentation may accomplish ALL BUT which of the following
        objectives?

        a)  Illustrate the amount of variation in the data.
        b)  Illustrate approximately where the mean is.
        c)  Allow comparison with similar data.
        d)  Will have the exact same shape regardless of what units are used on
            the axes.

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2890-3

    Q:  A sample is:

             a.  a number resulting from the manipulation of raw data
                 according to specified rules.
             b.  a subset of a population.
             c.  a characteristic of a population which is measurable.
             d.  a complete set of individuals, objects, or measurements
                 having some common observable characteristic.
             e.  none of the above.

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Answers:

21-1

    A:  a.  The mean of distribution C differs from the means of distributions
            A and B.

        b.  Distribution B has the smallest standard deviation.

        c.  Yes, it is likely that the mean of distribution A corresponds
            closely with the mode of distribution B.

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40-2

    A:  Definition:  The value divided when division is carried out.
        Example:     The expression 12/5 or (12 divided by 5) indicates that 12
                     is to be divided by 5.  12 is the numerator.

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41-1

    A:  Definition:  The value that "goes into" the value divided when division
                     is carried out or the value below the division symbol in a
                     fraction.
        Example:     The expression 12/5 or (12 divided by 5) indicates that 12
                     is to be divided by 5.  5 is the denominator.  It is the
                     number that "goes into" 12.

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46-4

    A:  One would examine previous weather records and note the relative fre-
        quency  of  90+  degree  days  in  Vermont,  and  100+ degree days in
        Florida. Thus, relative frequencies are one method of estimating  the
        probability  of  each  event.   (Note:  The smallest frequency is the
        more unusual event.)

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50-1

    A:  a.  In a series of such guesses, the sum of the errors in one
            direction will balance the sum of the errors in the other
            direction.

            Answers b. and c. are not necessarily true with distributions
            other than normal distributions.

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715-1

    A:  (3)  Column c is correct

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717-1

    A:  b.  Ms. Quincy's class is less heterogeneous than Ms. Sweetwater's.

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723-1

    A:  b.  a histogram

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1014-1

    A:  1.  the same

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1016-1

    A:  E. 4 and 3.5

        Mean = (1+7+3+3+6+4)/6
             = 4

        Data arranged in ascending order: 1,3,3,4,6,7
        Median = (3+4)/2
               = 3.5

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1021-1

    A:  a.  21

        Median is not sensitive to the relative magnitude of the scores but is
        determined by their rank ordering, which is not affected by this change.

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1403-1

    A:   i)   671/11 =  61.0,    (d)
        ii)  1082/10 = 108.2,    (b)

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1562-1

    A:  d.  All the elements in the population are 25.

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1719-1

    A:  False.  There are many distributions  for  which this statement is
        false, however it is true for distributions that are approximately
        normal.

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1743-1

    A:  (5)  20/6 = 3.33

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1743-2

    A:  1.  skewed negatively.

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1745-1

    A:  c. mean

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1745-3

    A:  a.  positively skewed.

            In a positively skewed distribution the mean is greater than the
            median, while in a negatively skewed distribution the mean is less
            than the median, and in a symmetrical distribution the mean is equal
            to the median.

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1746-1

    A:  b.  mean.

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1746-3

    A:  d.  standard deviation

            Standard deviation is a measure of dispersion among the data.

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1797-2

    A:  c.  it will be increased by 3 points

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1799-2

    A:  (a)  always equal to zero.

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1802-3

    A:       (E.)  It may refer to any of these.

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1803-1

    A:  d.  central tendency.

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1805-2

    A:  d.  1

            mean = (SUM(X(I)*Freq(I)))/SUM(Freq(I))

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1810-1

    A:  (c)  5.00

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1811-1

    A:  c.  8

            (-5 + 10 + 20 + 5 + 10)/5 = 8

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1820-3

    A:  a.  zero.

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1821-1

    A:  d.  (3*2 + 2*4 + 2*6 + 3*7)/10

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1838-1

    A:  a.         SCORE       |  FREQUENCY
                ------------------------------
                   90 - 100    |      2
                   80 -  89    |      3
                   70 -  79    |     22
                   60 -  69    |     16
                   50 -  59    |      6
                   40 -  49    |      1

                                -----
                               |     |
                               |     |
                          -----|     |
                         |     |     |
                         |     |     |
                         |     |     |
                    -----|     |     |
                   |     |     |     |
                   |     |     |     |-----
                   |     |     |     |     |
              -----|     |     |     |     |-----
             |  |  |  |  |  |  |  |  |  |  |  |  |
          -----------------------------------------------
               45    55    65    75    85    95

        b.  XBAR = 69.94
            Median = 77.5
            Interquantile Range = 75 - 65 = 10
            Variance = 91.65

        c.  Insufficient information is given, but one assumes from part (b)
            that it is a sample.

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1839-2

    A:  a.  Company          Mean          Variance          St. Dev.
                 (SUM X(i))/n=XBAR   S**2=(SUM(X-XBAR)**2)/n-1     S=SQRT(VAR.)

               A           25/5=5              0                 0
               B           25/5=5         2/4=1/2=.5         SQRT( 1/2 )=.707
               C           25/5=5         64/4=16            SQRT( 16 )=4
               D           25/5=5         32/4=8             SQRT(8)=2.83
               E           50/10=5        32/9=3.55          SQRT( 3.55)=1.89
               F           50/10=5        70/9=7.78           SQRT(7.78)=2.79

        b.  This question may have a variety of answers.  The decision would
        depend on the purpose.  If it was important to have as little
        variability as possible when selling 5 inch hot dogs, company A
        would be best since it has the least variability.  However, if you
        could profit from selling hot dogs in a variety of lengths, company
        F might prove best since it shows a lot of variability and produces hot
        dogs ranging from 9 to 3 inches in length.

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1840-1

    A:  a.  XBAR(height) = 1392/20 = 69.6
            XBAR(length) = 64.9/20 =  3.245

        b.  S**2(height) = (SUM(X - 69.6)**2)/19
                         = 12.96       1.96
                            2.56       1.96
                             .36       5.76
            deviations      2.56        .36
            from the        1.96       1.96
            mean squared   11.56        .16
            are:            6.76       5.76
                            2.56        .36
                           21.16        .16
                            5.76        .16

            S**2(height) = 86.8/19 = 4.568

            S**2(length) = (SUM(X - 3.245)**2)/19
                         =   .06        .002
                             .065       .198
                             .024       .119
            deviations       .065       .021
            from the         .207       .021
            mean squared     .002       .003
            are:             .065       .002
                             .024       .065
                             .021       .119
                             .065       .021

            S**2(length) = 1.169/19 = .06

        c.  S(height) = SQRT(4.568) = 2.137
            S(length) = SQRT(.06)   =  .25

        d.  FREQUENCY PLOTS: 
                       |
                       |                    MALE HEIGHTS
                       |
                       |
                     6 +
            Frequency  |
                     5 +
                       |
                     4 +                                  x
                       |
                     3 +                   x    x    x         x
                       |
                     2 +
                       |
                     1 +    x    x    x                             x
                       |
                       -----+----+----+----+----+----+----+----+----+----+-->
                           65   66   67   68   69   70   71   72   73   74
                                                Inches
 
                       |
                       |
                       |               LENGTH OF INDEX FINGER
                       |
                     6 +
            Frequency  |
                     5 +                                       x
                       |
                     4 +                   x
                       |
                     3 +                        x
                       |
                     2 +         x                        x
                       |
                     1 +    x         x              x                   x
                       |
                       -----+----+----+----+----+----+----+----+----x----+-->
                           2.8  2.9  3.0  3.1  3.2  3.3  3.4  3.5  3.6  3.7
                                                Inches

            NOTE:  To complete frequency plots, connect x's with straight lines.

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1847-2

    A:  a.  Worker B appears to be more consistent in the time he requires
            to complete the job, since he has a smaller variance.

        b.  Worker B appears to be faster in completing the job, since he
            has a smaller mean.  (You could actually test this.)

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1849-1

    A:  No--the estimate that he would get using the mean number per
        month would most likely be accurate enough, without having to
        go to the extra expense of another study.  Presumably the mean
        number of hours lost per month is equal to the total number
        of hours lost divided by 12, so it's not difficult to
        calculate the total.

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1855-4

    A:  NO, because mean and standard deviation may not specify the distribu-
        tions completely.  Even if they do so, (as in normal distributions)
        there is no relation between mean and standard deviation.  Hence, if
        there is a calculation mistake, it is not detectable by the given in-
        formation.  In fact, for the exponential distribution, the mean exactly
        equals the standard deviation.

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1862-1

    A:  (1)  0

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1862-2

    A:  (1)  2.5

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1864-1

    A:  (a)  2.0

             SS = 2.0 and n - 1 = 1
             S(Y)**2 = 2.0/1 = 2.0

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1866-1

    A:  b.  variability.

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1867-1

    A:  b.  [SUM(X(i)-XBAR)]/[n]

            SUM(X(i)-XBAR) always equals zero.

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1874-1

    A:  True

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1876-1

    A:  2.  SUM(X - XBAR) = 0

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1878-1

    A:  a.  remain the same.

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1878-2

    A:  c.  increase the standard deviation.

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1879-1

    A:  a.  3

            The variance is equal to the standard deviation squared.

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1879-2

    A:  4.  none of these

            Correct answer:  10.

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1879-3

    A:  a.  variance = (standard deviation)**2

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1883-1

    A:  e.  Any SBP reduction score between 0 and 20 is within one standard
            deviation of the sample mean.

            10 +/- SQRT(25) is the interval from 5 to 15.

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1884-3

    A:  a. A offers a more homogeneous product.

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1885-3

    A:  d.  Standard deviation

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1886-1

    A:  a.  2
            For the calculation of the standard deviation it does not make any
            difference if the present ages are 1,2,3,4,5,6, and 7 years or 15,
            16,17,18,19,20, and 21, or whatsoever.  So take 1,2,3,4,5,6, and 7
            and calculated S = SQRT([[X-MU]**2]/[n]).

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1887-4

    A:  Variance = 600/24 = 25
        Standard deviation = SQRT(25) = 5

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1888-2

    A:  XBAR = (1+1+7+13+13)/5 = 7
                                                  TOTAL
             X         1     1     7    13    13    35
           X-XBAR     -6    -6     0     6     6     0
        (X-XBAR)**2   36    36     0    36    36   144

        S= SQRT (144/4)
         = SQRT (36)
         = 6

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1889-2

    A:  Variance = (SUM((X - XBAR)**2))/(n - 1)
                 = 13.5

        Standard Deviation = SQRT[SUM((X - XBAR)**2)/(n - 1)]
                           == 3.67

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1891-3

    A:  On inspection, data set S has the larger sample standard deviation.
        By calculation:  S(S) = 2.58
                         S(T) = 1.27

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1896-3

    A:  True.

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1897-2

    A:  False.  The standard deviation is a measure of spread in a distribution.

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1899-1

    A:  True.

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1901-2

    A:  True.

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1907-3

    A:  c.  the variance only when the mean equals zero.

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1910-1

    A:  b)  108.2

            Sample Variance = (1/(N-1))SUM(i=1,11)([Y(i)-YBAR]**2)
                            = (1/(11 - 1))(1082)
                            = (1/10)(1082)
                            = 108.2

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1911-1

    A:  D. 5

        S**2 = SUM[(X(i) - XBAR)**2/(n-1)], where XBAR is the mean of the data
             = (9+9+1+1+4+0)/5
             = 24/5 = 4.8

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1914-1

    A:  d.  122.5

            Variance = [SUM(i=1,n)((X(i) - XBAR)**2)]/[n - 1]
                     = ([(47.1-40.1)**2] + [(33.1-40.1)**2] + [(26.1-40.1)**2] +
                       [(40.1-40.1)**2] + [(54.1-40.1)**2])/[4]
                     = 490/4
                     = 122.5

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1916-1

    A:  c.  16

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1920-1

    A:  d.  farthest from the mean.

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1920-3

    A:  b.  Because otherwise the variance would always be equal to 0.
            Note:  SUM(i=1,n)(X-XBAR) = 0

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1950-1

    A:  False.  The variance of a set of negative numbers is positive.

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2000-1

    A:  a.  The mean is greater than the median, indicating the histogram
            would be skewed with its tail to the right.

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2002-1

    A:  1)  A picture is worth a thousand words, i.e. a visual display is a good
            way to summarize a large data set.

        2)  Histograms  give  some  feeling for the overall shape of the  data,
            something that reporting  XBAR  and  S  cannot give, i.e. skewness,
            kurtosis, range.

        3)  Relative histograms and frequency polygons are estimates of proba-
            bility functions.

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2003-1

    A:  1.  FREQUENCY TABLE

            Score                Midpoint                Frequency

            37-40                  38.5                      2
            33-36                  34.5                      2
            29-32                  30.5                      1
            25-28                  26.5                      3
            21-24                  22.5                      3
            17-20                  18.5                      2
            13-16                  14.5                      3
             9-12                  10.5                      1
             5-8                    6.5                      4
             1-4                    2.5                      0

        2.  HISTOGRAM

            Frequency
               |
               |
               |
             5 +
               |
               |
             4 +    _____
               |    |   |
               |    |   |
             3 +    |   |   _____   _________
               |    |   |   |   |   |   |   |
               |    |   |   |   |   |   |   |
             2 +    |   |   |   |___|   |   |   _________
               |    |   |   |   |   |   |   |   |   |   |
               |    |   |   |   |   |   |   |   |   |   |
             1 +    |   |___|   |   |   |   |___|   |   |
               |    |   |   |   |   |   |   |   |   |   |
               |    |   |   |   |   |   |   |   |   |   |
               -+---+---+---+---+---+---+---+---+---+---+-------->
               .5      8.5    16.5    24.5    32.5    40.5
                   4.5    12.5    20.5    28.5    36.5

                          Final Examination Scores


        3.  The real or exact limits of the lowest interval are 4.5 - 8.5.

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2005-1

    A:  a.  Y    Cumulative Rel. Freq.
            -    ---------------------
            0           5/100
            1          30/100
            2          60/100
            3          85/100
            4         100/100

        b.                 |
                           |
                        30 +       -----
                           |       |   |
                           +   ----|   |----
                           |   |   |   |   |
                        20 +   |   |   |   |
            Relative       |   |   |   |   |
            Frequency      +   |   |   |   |----
                           |   |   |   |   |   |
                        10 +   |   |   |   |   |
                           |   |   |   |   |   |
                           +---|   |   |   |   |
                           |   |   |   |   |   |
                           --+---+---+---+---+-------->  Y
                             0   1   2   3   4

        c.  Median = 1.5 + (20/30)(1.0) = 2.17
            Mode = 2

            Mean = [0(5) + 1(25) + 2(30) + 3(25) + 4(15)]/100 = 220/100 = 2.2

        d.  Prob(Y >= 2) = (30/100) + (25/100) + (15/100) = 70/100 = .70 = 70%

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2006-3

    A:   .4                x

         .3
                      x         x
         .2

         .1
                 x                   x
         0  x                             x
           _____________________________________
           0-1  1-2  2-3  3-4  4-5  5-6  6-7

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2008-1

    A:  a)  Class      Freq.      Rel. Freq.

             1-4         4          4/25
             5-8         5          5/25
             9-12        6          6/25
            13-16        6          6/25
            17-20        4          4/25

            Totals      25         25/25

        b)            |
                      |
                10/25 +
                      |
             Relative |
            Frequency |
                      |                -----------------
                 5/25 +        --------|       |       |
                      |--------|       |       |       |--------
                      ||       |       |       |       |       |
                      ||       |       |       |       |       |
                      ||       |       |       |       |       |
                      --+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+----->
                        1     4 5     8 9    12 13   16 17   20
                                        X Values


        c)  1.  Sometimes it is easier to get the mean and variance
                (group method -- by hand).

            2.  Visual check on calculation of mean and variance.

            3.  Easier for lay person (specialist also) to see what values
                are likely and what values are unlikely in a population.

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2009-3

    A:  The primary problem is that the vertical axis does not have equally
        spaced intervals.  For example, a constant distance on the axis re-
        presents jumps of 5, 25, and 70 units.

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2011-1

    A:             |
                   |                    FEMALES
        Frequency  |
                   |                    -----
                   |                ----|   |----
                   |            ----|   |   |   |----
                   |        ----|   |   |   |   |   |----
                   |    ----|   |   |   |   |   |   |   |----
                   |    |   |   |   |   |   |   |   |   |   |
                   |    |   |   |   |   |   |   |   |   |   |
                   -----------------------+--------------------------->
                                         XBAR


       |
                   |                     MALES
        Frequency  |
                   |
                   |                                 -----
                   |                                 |   |
                   |                                 |   |
                   |                                 |   |
                   |                             ----|   |----
                   |                             |   |   |   |
                   |                             |   |   |   |
                   |                         ----|   |   |   |----
                   |                         |   |   |   |   |   |
                   |                         |   |   |   |   |   |
                   |                         |   |   |   |   |   |
                   |                         |   |   |   |   |   |
                   ------------------------------------+-------------->
                                                      YBAR

        Histogram for males should be taller and thinner and shifted to the
        right of that for females.  The areas of the two histograms should be
        the same.

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2012-1

    A:  1.  Too few intervals to give meaningful results.
        2.  Open ended interval
        3.  Intervals of unequal length.

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2014-1

    A:  Definition:  A graph indicating frequencies or relative frequencies of
                     values (or value classes) of a random variable.

        Example:     Suppose that we interviewed 10 sultans to discover how
                     many wives each sultan enjoyed.  Suppose that the results
                     were:
                            1 sultan had no wives
                            4 sultans had two wives
                            3 sultans had three wives, and
                            2 sultans had four wives.

                     Then the appropriate histogram would be:

                               |
                     Number of |
                     Sultans   |
                               |
                             4 +           -------
                               |           |     |
                             3 +           |     |------
                               |           |     |     |
                             2 +           |     |     |------
                               |           |     |     |     |
                             1 +------     |     |     |     |
                               |     |     |     |     |     |
                               ---+-----+-----+-----+-----+--------->
                                  0     1     2     3     4
                                       Number of Wives

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2015-1

    A:  a.  19/30

            30 students scored more than 33(5+17+8 = 30) of which
            19(4+10+5) were in the age range 104-113 months.

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2016-1

    A:  a.  both will have the same values on the horizontal axis.

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2017-1

    A:  c.  82

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2019-1

    A:  b.  a relative frequency distribution.

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2019-3

    A:  b.  10; (190-40)/15 = 10

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2020-1

    A:  a.  Negatively skewed (skewed to the left),
            because they score higher in general.

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2020-2

    A:  a)  The value of the measurement and the number of individuals with
            that value.

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2030-1

    A:  True.

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2033-2

    A:  d. has earned a score equal to or better than 40% of the
           persons in his class.

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2033-3

    A:  c. 70

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2034-1

    A:  (d)

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2036-1

    A:  1)  c.  38 frequencies are spread out throughout the interval.
        2)  e.  97.5% of the cases fall below a score of 74.5.
        3)  e.  47.5

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2037-1

    A:  c.  the score below which k% of the cases fall.

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2038-1

    A:  b.  78th percentile.

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2038-2

    A:  d.  Individuals in reference group B generally scored lower
            on the test than those in reference group A.

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2042-2

    A:  2.  40

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2043-2

    A:  b. between Q(1) and Q(3)

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2044-1

    A:  c.  14% of those taking the test got scores ranging between Tom's
            and Bill's.

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2045-1

    A:    (i)  b.  12
          (ii)  a.  skewed to the left

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2050-4

    A:  It tells you that 60% of the sample has values less than or equal
        to 1468.3.

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2053-3

    A:  True.

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2053-4

    A:  False. If the percentile rank for the value 60 is 40, this means
        that 60% of the observations will fall above 60.

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2057-4

    A:  a)  Investigation of characteristics of each observation.

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2065-1

    A:  1.  negative, because the mean is below the median.  The two low
            values, (22, 23), are primarily responsible.

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2066-1

    A:  c.  Skewed right (positively skewed)

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2119-2

    A:  d)  Will have the exact same shape regardless of what units are used on
            the axes.

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2890-3

    A:  b.  a subset of a population.

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Return to Brian Schott @ GSU

Identification:

21-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
PROBABILITY
        MEAN              STANDARDDEVIATIO  DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 2    General
                ***Multiple Parts***

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40-2

Based upon item submitted by J. Warren - UNH
        Definition
BASICTERMS/PROB
        I650I             PROBABILITY

T= 2    Comprehension
D= 1    General

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41-1

Based upon item submitted by J. Warren - UNH
        Definition
BASICTERMS/PROB
        I650I             PROBABILITY

T= 2    Comprehension
D= 1    General

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46-4

Item is still being reviewed
        Short Answer
PROBMODELS        TESTING
        PROBABILITY       CONCEPT           STATISTICS

T= 2    Comprehension
D= 2    General             Natural Sciences

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50-1

Item is still being reviewed
        Multiple Choice
PROBDISTRIBUTION  MEAN
        PROBABILITY       DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 3    General

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715-1

Item is still being reviewed
        Multiple Choice
FREQDIAGRAM       STATISTICS
        DESCRSTAT/P       PARAMETRIC

T= 2    Computation
D= 2    General

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717-1

Item is still being reviewed
        Multiple Choice
BASICTERMS/STATS  VARIABILITY/P
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 2    General             Education

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723-1

Item is still being reviewed
        Multiple Choice
BASICTERMS/STATS  HISTOGRAM         FREQTABLE
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Comprehension
D= 2    General

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1014-1

Based upon item submitted by J. Inglis
        Multiple Choice
MEAN              MEDIAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        DESCRSTAT/NP      NONPARAMETRIC

T= 2    Comprehension
D= 1    General

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1016-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
MEDIAN
        MEAN              DESCRSTAT/NP      NONPARAMETRIC
        STATISTICS        DESCRSTAT/P       PARAMETRIC

T= 2    Computation
D= 1    General

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1021-1

Based upon item submitted by J. Inglis
        Multiple Choice
MEDIAN
        DESCRSTAT/NP      NONPARAMETRIC     STATISTICS

T= 2    Comprehension
D= 2    General

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1403-1

Based upon item submitted by R. F. Tate - U. of Oregon
        Multiple Choice
VARIANCE          MEAN              UNBIASEDNESS
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        ESTIMATION        CONCEPT

T= 5    Computation
D= 2    General
                ***Multiple Parts***

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1562-1

Item is still being reviewed
        Multiple Choice
POPULATION        MEAN              VARIANCE
        CONCEPT           STATISTICS        DESCRSTAT/P
        PARAMETRIC

T= 2    Comprehension
D= 2    General

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1719-1

Item is still being reviewed
        True/False
STANDARDDEVIATIO  TCHEBYSHEFFSTHM
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        CONCEPT

T= 2    Comprehension
D= 4    General

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1743-1

Item is still being reviewed
        Multiple Choice
CENTRALTENDENCY   MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 1    General

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1743-2

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
CENTRALTENDENCY   SKEWNESS/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1745-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
MEAN              CENTRALTENDENCY
        MODE              MEDIAN            DESCRSTAT/P
        PARAMETRIC        STATISTICS        DESCRSTAT/NP
        NONPARAMETRIC

T= 2    Comprehension
D= 2    General

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1745-3

Based upon item submitted by R. Pruzek - SUNY at Albany
        Multiple Choice
CENTRALTENDENCY
        SKEWNESS/P        DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 3    General

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1746-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
CENTRALTENDENCY   MEAN
        MEDIAN            MODE              DESCRSTAT/P
        PARAMETRIC        STATISTICS        DESCRSTAT/NP
        NONPARAMETRIC

T= 2    Comprehension
D= 2    General

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1746-3

Based upon item submitted by J. Inglis
        Multiple Choice
CENTRALTENDENCY   STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1797-2

Item is still being reviewed
        Multiple Choice
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 2    General

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1799-2

Item is still being reviewed
        Multiple Choice
VARIABILITY/P     MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1802-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
MEAN
        CENTRALTENDENCY   I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1803-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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1805-2

Item is still being reviewed
        Multiple Choice
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 4    General

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1810-1

Item is still being reviewed
        Multiple Choice
MEAN
        SIMPLEDATASET     DESCRSTAT/P       PARAMETRIC
        STATISTICS        MISCELLANEOUS

T= 2    Computation
D= 1    General

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1811-1

Item is still being reviewed
        Multiple Choice
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 1    Biological Sciences

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1820-3

Item is still being reviewed
        Multiple Choice
MEAN              VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General             Education

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1821-1

Item is still being reviewed
        Multiple Choice
MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General             Education

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1838-1

Based upon item submitted by K. Gorowara - Wright State U.
        Numerical Answer
HISTOGRAM         MEAN              VARIANCE
        FREQTABLE         VARIABILITY/P     PERCENTILE
        RANGE             DESCRSTAT/P       PARAMETRIC
        STATISTICS        VARIABILITY/NP    DESCRSTAT/NP
        NONPARAMETRIC

T=15    Computation
D= 2    General             Education
                ***Calculator Necessary***
                ***Graph or Chart Necessary***
                ***Multiple Parts***

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1839-2

Item is still being reviewed
        Numerical Answer
MEAN              VARIANCE          STANDARDDEVIATIO
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T=10    Computation     Comprehension
D= 4    General             Business
                ***Calculator Necessary***
                ***Multiple Parts***

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1840-1

Item is still being reviewed
        Numerical Answer
MEANFREQDIAGRAM   VARI              STANDARDDEVIATIO
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS        I650/TEMPORARY    MISCELLANEOUS

T=10    Computation
D= 3    General
                ***Calculator Necessary***
                ***Multiple Parts***

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1847-2

Item is still being reviewed
        Short Answer
VARIANCE          MEAN
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 2    General             Business
                ***Multiple Parts***

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1849-1

Item is still being reviewed
        Short Answer
MEAN
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 2    General             Business

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1855-4

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
MEAN              STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1862-1

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
VARIANCE          VARIABILITY/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 1    General

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1862-2

Item is still being reviewed
        Multiple Choice
VARIANCE          VARIABILITY/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 1    General

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1864-1

Based upon item submitted by H. B. Christensen - BYU
        Multiple Choice
VARIABILITY/P     VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 2    General

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1866-1

Item is still being reviewed
        Multiple Choice
PERCENTILE        VARIABILITY/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 4    General

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1867-1

Item is still being reviewed
        Multiple Choice
VARIABILITY/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1874-1

Item is still being reviewed
        True/False
STANDARDDEVIATIO  VARIABILITY/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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1876-1

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
VARIANCE          STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 2    General

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1878-1

Item is still being reviewed
        Multiple Choice
VARIANCE          STANDARDDEVIATIO
        SPECIALCASE/PROB  DESCRSTAT/P       PARAMETRIC
  STATISTICS        MISCELLANEOUS

T= 2    Computation     Comprehension
D= 4    General

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1878-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
STANDARDDEVIATIO
        PROBDISTRIBUTION  DESCRSTAT/P       PARAMETRIC
        STATISTICS        PROBABILITY

T= 2    Comprehension
D= 4    General

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1879-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
VARIANCE          STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 1    General

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1879-2

Item is still being reviewed
        Multiple Choice
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1879-3

Item is still being reviewed
        Multiple Choice
VARIANCE          STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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1883-1

Item is still being reviewed
        Multiple Choice
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    Biological Sciences

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1884-3

Item is still being reviewed
        Multiple Choice
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1885-3

Item is still being reviewed
        Multiple Choice
STANDARDDEVIATIO
        MEDIAN            MODE              RANGE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        DESCRSTAT/NP      NONPARAMETRIC     VARIABILITY/NP

T= 2    Comprehension
D= 2    General             Education

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1886-1

Item is still being reviewed
        Multiple Choice
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 2    General

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1887-4

Based upon item submitted by D. V. Sisson - Utah State
        Numerical Answer
VARIANCE          COEFFVARIATION    STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation     Application
D= 3    General
                ***Calculator Necessary***
                ***Multiple Parts***

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1888-2

Based upon item submitted by R. Shavelson - UCLA
        Numerical Answer
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 1    General

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1889-2

Based upon item submitted by D. F. Butcher - W. Virginia U.
        Numerical Answer
VARIANCE          STANDARDDEVIATIO
        SIMPLEDATASET     DESCRSTAT/P       PARAMETRIC
        STATISTICS        MISCELLANEOUS

T= 5    Computation
D= 2    General
                ***Calculator Necessary***

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1891-3

Based upon item submitted by R. Shavelson - UCLA
        Short Answer
STANDARDDEVIATIO
        VARIABILITY/P     SIMPLEDATASET     I650I
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation     Comprehension
D= 3    General

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1896-3

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
STANDARDDEVIATIO
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 2    General

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1897-2

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
STANDARDDEVIATIO
        POPULATIONMODELS  DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 4    General

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1899-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1901-2

Item is still being reviewed
        True/False
STANDARDDEVIATIO
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General             Education

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1907-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
VARIANCE
        MODEL             STANDARDDEVIATIO  DESCRSTAT/P
        PARAMETRIC        STATISTICS        MISCELLANEOUS

T= 2    Computation
D= 1    General

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1910-1

Based upon item submitted by R. F. Tate - U. of Oregon
        Multiple Choice
VARIANCE          SAMPLE
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        SAMPLING

T= 5    Comprehension   Computation
D= 3    General

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1911-1

Based upon item submitted by F. J. Samaniego - UC Davis
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 1    General

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1914-1

Item is still being reviewed
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Computation
D= 2    General
                ***Calculator Necessary***

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1916-1

Item is still being reviewed
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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1920-1

Item is still being reviewed
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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1920-3

Item is still being reviewed
        Multiple Choice
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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1950-1

Based upon item submitted by R. Pruzek - SUNY at Albany
        True/False
VARIANCE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2000-1

Based upon item submitted by A. Matthews - U. Mass.
        Multiple Choice
HISTOGRAM         SKEWNESS/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General             Biological Sciences
                ***Graph or Chart Necessary***

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2002-1

Based upon item submitted by D. F. Butcher - W. Virginia U.
        Essay
HISTOGRAM         FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    General

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2003-1

Item is still being reviewed
        Numerical Answer
FREQTABLE         HISTOGRAM         FREQDIAGRAM
        CLASSINTERVAL     SIMPLEDATASET     I650I
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Computation
D= 4    General
                ***Multiple Parts***

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2005-1

Based upon item submitted by W. Federer - Cornell
        Numerical Answer
HISTOGRAM         FREQTABLE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Computation
D= 3    General
                ***Multiple Parts***

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2006-3

Based upon item submitted by J. Warren - UNH
        Numerical Answer
HISTOGRAM
        NORMAL            I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS        PROBDISTRIBUTION
        PROBABILITY

T= 5    Comprehension
D= 2    General

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2008-1

Based upon item submitted by R. E. Lund - Montana State U.
        Short Answer
HISTOGRAM         FREQDIAGRAM       FREQTABLE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Computation     Comprehension
D= 3    General
                ***Multiple Parts***

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2009-3

Based upon item submitted by A. Bugbee - UNH
        Short Answer
HISTOGRAM         GRAPH/PICTOGRAPH
        COMMONPITFALLS    BARCHART/P        DESCRSTAT/P
        PARAMETRIC        STATISTICS        MISCELLANEOUS

T= 2    Comprehension
D= 2    General

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2011-1

Item is still being reviewed
        Short Answer
HISTOGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T=10    Comprehension
D= 3    General

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2012-1

Item is still being reviewed
        Short Answer
HISTOGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    General

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2014-1

Based upon item submitted by J. Warren - UNH
        Definition
HISTOGRAM
        BASICTERMS/STATS  I650I             DESCRSTAT/P
        PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 2    General

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2015-1

Based upon item submitted by B. Weir - N. C. State & Massey Univ.
        Multiple Choice
FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Application
D= 2    Education

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2016-1

Based upon item submitted by A. Bugbee - UNH
        Multiple Choice
FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2017-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
PERCENTILE        FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2019-1

Based upon item submitted by J. Inglis
        Multiple Choice
FREQDIAGRAM
        HISTOGRAM         CUMULATIVEFN      DESCRSTAT/P
        PARAMETRIC        STATISTICS        PROBDISTRIBUTION
        PROBABILITY

T= 2    Comprehension
D= 2    General

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2019-3

Item is still being reviewed
        Multiple Choice
FREQDIAGRAM       FREQTABLE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation
D= 2    General             Education

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2020-1

Item is still being reviewed
        Multiple Choice
SKEWNESS/P        FREQDIAGRAM       TESTCONSTRUCTION
        DESCRSTAT/P       PARAMETRIC        STATISTICS
        TESTTHEORY

T= 2    Comprehension
D= 3    General             Education

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2020-2

Item is still being reviewed
        Multiple Choice
FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 3    General

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2030-1

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
FREQDIAGRAM
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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2033-2

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    Education           General

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2033-3

Item is still being reviewed
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension   Computation
D= 2    Education           General

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2034-1

Based upon item submitted by R. Shavelson - UCLA
        Multiple Choice
PERCENTILE
        I650I             DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Computation
D= 3    General             Education

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2036-1

Item is still being reviewed
        Multiple Choice
FREQTABLE         PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension   Computation
D= 3    General
                ***Multiple Parts***

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2037-1

Item is still being reviewed
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2038-1

Item is still being reviewed
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2038-2

Based upon item submitted by W. J. Hall - Univ. of Rochester
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2042-2

Based upon item submitted by J. Inglis
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 3    General

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2043-2

Item is still being reviewed
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2044-1

Item is still being reviewed
        Multiple Choice
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General             Education

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2045-1

Item is still being reviewed
        Multiple Choice
PERCENTILE        GRAPH/PICTOGRAPH  SKEWNESS/P
        MEDIAN            FREQDIAGRAM       DESCRSTAT/P
        PARAMETRIC        STATISTICS        DESCRSTAT/NP
        NONPARAMETRIC

T= 5    Computation     Comprehension
D= 3    General             Education
                ***Graph or Chart Necessary***
                ***Multiple Parts***

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2050-4

Item is still being reviewed
        Short Answer
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 5    Comprehension
D= 2    General

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2053-3

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2053-4

Based upon item submitted by W. J. Hall - Univ. of Rochester
        True/False
PERCENTILE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 2    General

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2057-4

Item is still being reviewed
        Multiple Choice
FREQTABLE
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Comprehension
D= 1    General

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2065-1

Item is still being reviewed
        Multiple Choice
SKEWNESS/P
        DESCRSTAT/P       PARAMETRIC        STATISTICS

T= 2    Computation     Comprehension
D= 1    General

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2066-1

Item is still being reviewed
        Multiple Choice
SKEWNESS/P
        PERCENTILE        DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 5    Comprehension
D= 5    General             Education

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2119-2

Item is still being reviewed
        Multiple Choice
TYPICALPIC/GRAPH  GRAPH/PICTOGRAPH
        MISCELLANEOUS     DESCRSTAT/P       PARAMETRIC
        STATISTICS

T= 2    Comprehension
D= 2    General

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2890-3

Item is still being reviewed
        Multiple Choice
SAMPLE
        SAMPLING          STATISTICS

T= 2    Comprehension
D= 1    General

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