Deck 4: Measures of Dispersion

Question 1

For the variable region of birth,which of the following should be used to measure dispersion?

A)the index of qualitative variation
B)the range
C)the average deviation
D)the variance

Answer 1

the index of qualitative variation

Question 2

The interquartile range would be an appropriate measure of dispersion for

A)nominal level variables.
B)continuous interval-ratio level variables only.
C)ordinal level variables.
D)discrete interval-ratio level variables only.

Answer 2

ordinal level variables.

Question 3

If a distribution of scores has a mean of 30 and a range of 0:

A)the variance is 30
B)the quartile deviation (Q)is 10
C)there is no dispersion in the distribution
D)the standard deviation is 1

Answer 3

there is no dispersion in the distribution

Question 4

For the variable gender,which of the following should be used to measure dispersion?

A)the index of qualitative variation
B)the range
C)the average deviation
D)the variance

Question 5

An advantage of the interquartile range (Q)over the range (R)is that it

A)can be used for nominal level variables.
B)includes the most extreme scores.
C)is based on only the middle 50% of the scores.
D)ignores the first and third quartiles.

Question 6

The second quartile (Q₂)is equal in value to

A)the mode.
B)the median.
C)the mean.
D)the range.

Question 7

Which of the following data sets shows the greatest variability?

A)9,10,11
B)0,5,9
C)50,60,170
D)31,33,35

Question 8

The index of qualitative variation (IQV)is the ratio of the actual variation in the scores to

A)One.
B)the maximum variation possible.
C)the minimum variation possible.
D)the number of scores.

Question 9

A "good" measure of dispersion should

A)use all scores in a distribution.
B)describe the average or typical deviation of the scores.
C)be easy to calculate and interpret.
D)all of the above

Question 10

The index of qualitative variation (IQV)varies from 0.00 to 1.00.Which of the IQV's below shows the greatest degree of homogeneity?

A)0.25
B)0.50
C)0.75
D)1.00

Question 11

The range (R)is found by subtracting the lowest from the highest score in the distribution.Therefore,R could NOT be found for

A)nominal level variables.
B)discrete variables.
C)ordinal level variables.
D)continuous variables.

Question 12

Measures of dispersion indicate the degree to which a set of scores is

A)heterogeneous.
B)ambiguous.
C)average.
D)typical.

Question 13

One problem with the range (R)as a measure of dispersion is that it

A)is very difficult to calculate.
B)ignores the most extreme scores.
C)can be used only for nominal level variables.
D)is based on only the most extreme scores.

Question 14

Measures of dispersion provide information about the

A)typical or most common score.
B)variety within the distribution of scores.
C)size of the sample.
D)adequacy of the selection criteria for the sample.

Question 15

If a test score lies at the first quartile,it is

A)higher than 25% of the scores.
B)the same as the median.
C)the same as the mode.
D)higher than 75% of the scores.

Question 16

The distances between the scores and the mean are called

A)deviations.
B)differences.
C)ranges.
D)summations.

Question 17

Your score on the test is the same as the third quartile (Q₃).You may conclude that

A)you scored higher than 75% of the people who took the test.
B)the distribution of the scores is skewed.
C)your score is 'typical' since it is the same value as the median.
D)you scored higher than 25% of the people who took the test.

Question 18

Between 1980 and 2005,the IQV for religious denomination in a society increased from 0.55 to 0.78.This means that the society is becoming

A)more religious.
B)more diverse in religious denomination.
C)less diverse in religious denomination.
D)more secular.

Question 19

Measures of central tendency (like the mean)and measures of dispersion (like the range)provide information about distributions of scores which is

A)contradictory.
B)redundant.
C)unnecessary.
D)complementary.

Question 20

For variables measured at the nominal level,an appropriate measure of dispersion is

A)the range
B)the average deviation
C)the index of qualitative variation
D)the mode

Question 21

When computing the standard deviation from grouped data,we must assume that the scores are clustered at the ____ of the interval.

A)mode
B)lower real limit
C)upper real limit
D)midpoint

Question 22

The income of a sample has been measured in dollars per year.Which of the following would be the preferred measure the dispersion for this variable? The

A)index of qualitative variation.
B)average deviation.
C)quartile deviation.
D)standard deviation.

Question 23

If the standard deviation of a group of scores is 0,

A)the range would be at a maximum value.
B)there is maximum variation in the scores.
C)there is no variation in the scores.
D)the mean is larger than the median.

Question 24

Since computation of the standard deviation requires addition,division,and other mathematical operations,it should be used for

A)interval-ratio level variables.
B)non-continuous variables at any level of measurement.
C)nominal level variables.
D)discrete variables only.

Question 25

The expression $\mathrm { S } \left( \mathrm { X } _ { \mathrm { i } } - \bar { X } \right.$ )² instructs us to

A)square the sum of the scores.
B)sum the squared scores.
C)sum the squared deviations.
D)square the summed deviations.

Question 26

The standard deviation (s)differs from the average deviation (AD)in that it

A)squares the deviations to eliminate minus values.
B)decreases in value as distributions become more heterogeneous.
C)does not use all the scores.
D)is based on the median rather than the mean.

Question 27

If a variable is interval-ratio in level of measurement,the preferred measure of dispersion would be

A)the mean.
B)the range.
C)the standard deviation.
D)the percentile.

Question 28

The lower limit for the standard deviation is 0;the upper limit is

A)the score of the mean.
B)the score of the median.
C)a function of the number of cases.
D)undefined;there is no upper limit.

Question 29

Which measure of dispersion is most important and most commonly used in social science research?

A)the range
B)the average deviation
C)the median
D)the standard deviation

Question 30

If you calculated the standard deviation for a distribution of 20 scores,removed the 5 highest scores and recalculated,the value of the standard deviation would

A)increase.
B)stay the same.
C)decrease.
D)be reduced by five.

Question 31

The average deviation (AD)is

A)always less than the standard deviation.
B)based on squaring the differences between the mean and scores.
C)actually a measure of central tendency,not dispersion.
D)not commonly useD.

Question 32

As a distribution of scores becomes more variable,the value of the standard deviation

A)decreases.
B)stays the same.
C)increases.
D)becomes unpredictable.

Question 33

The expression S(X_i - $\bar { X }$
)instructs us to

A)sum the scores.
B)sum the scores and then subtract the mean.
C)subtract every "ith" score from the mean.
D)subtract the mean from each score and add up the deviations.

Question 34

If the variance of a distribution is 16,the mean is 12,and the number of cases is 24,the standard deviation is

A)4
B)6
C)8
D)12

Question 35

When computing the standard deviation from grouped data,the sum of the deviations is approximated by using the ____ of the intervals.

A)midpoints
B)lower real limits
C)upper real limits
D)all of the above

Question 36

If distribution A and distribution B have the same mean,but A has a larger standard deviation,we may conclude that

A)the medians of both distributions would be the same.
B)distribution B has a range of 0.
C)A has a greater degree of dispersion.
D)distribution B displays more variety.

Question 37

The sum of the squared deviations around the mean for a distribution of 10 scores is 1000.The standard deviation

A)is 10.
B)is 100.
C)is 1.
D)can't be determined from this information.

Question 38

When you subtract the value of the mean from each score in a distribution and then add the results,the sum will be

A)0.
B)the standard deviation.
C)the variance.
D)a positive number.

Question 39

The age of a sample has been measured in years.Which of the following would be the preferred measure the dispersion for this variable?

A)the index of qualitative variation
B)the average deviation
C)the quartile deviation
D)the standard deviation

Question 40

The average deviation (AD)is based on

A)squaring the differences between the score and the mean.
B)ignoring the signs of the differences between the scores and the mean.
C)subtracting each score from the median.
D)subtracting each score from the mode.

Question 41

According to the data presented in the text,incomes in the U.S.are

A)falling for the average family.
B)rising for everyone except the very rich.
C)decreasing in dispersion (income inequality is decreasing).
D)increasing in dispersion (income inequality is increasing).

Question 42

Since the 1960s,the income associated with the 80^th percentile has ____ and the income associated with the 20^th percentile has ____.

A)risen,risen
B)stayed roughly the same,risen
C)fallen,risen
D)risen,stayed roughly the same

Question 43

The scores below are from the same final exam given in a math class in two different years.Compute the mean and median (if necessary)and the range and standard deviation of these scores.Using these statistics,describe the differences in the two sets of scores.

Question 44

If male and female college students work an average of 15 hours per week during the school year and the standard deviation is 5.4 for male students and 2.3 for female students,what may we conclude?

A)males are more heterogeneous on this variable
B)females are more heterogeneous on this variable
C)the median number of hours worked is the same
D)the modal number of hours worked is the same

Question 45

The information below compares the final exam grades for 2 biology classes:
$\begin{array}{|l|l|}\hline \text { Class 1 } & \text { Class } 2 \\\hline & \\\bar{X} & \bar{X} \\\\=80.2 & =81.3 \\\hline \mathrm{s}=12.1 & \mathrm{s}=6.7 \\\hline \mathrm{N}=25 & \mathrm{~N}=23 \\\hline\end{array}$
What may we conclude? Class 1

A)is more homogeneous.
B)is more heterogeneous.
C)was a better class.
D)had no grade higher than a 90.

Question 46

Some information about auto theft rates (number of auto thefts per 100,000 population)for a sample of 178 cities in two different years is summarized below.Express this statistical information in words.What changes were there in the overall shape of the distribution of this variable? In central tendency? In dispersion?

Question 47

The greater the skew of a distribution of scores,

A)the lower the value of the standard deviation.
B)the higher the value of the standard deviation.
C)the lower the value of the range.
D)None of the above.Measures of dispersion are not affected by skew.

Question 48

If male and female college students have the same mean GPA,but the standard deviation for females is much larger,you may conclude that

A)males are smarter than females.
B)modal GPAs for both groups would be the same.
C)median GPAs for both groups would be the same.
D)there is more variability among female students with respect to GPA.

Question 49

Which of the following is a correct description of the distribution of income in the US since the 1960s?

A)the mean income has risen but the median has fallen
B)both the mean and the median have risen but the mean has increased more
C)there is a noticeable negative skew in the distribution
D)the distribution has grown less variable

Question 50

Which of the following is true? Since the 1960s,

A)the distribution of income has become more heterogeneous.
B)average income has fallen.
C)median income increased until the 1990s and then fell.
D)the distribution of income has become more homogeneous

Question 51

The text presents information on the central tendency and dispersion of income in the U.S.Dispersion is measured by

A)the standard deviation.
B)the difference between the 20^th and 80^th percentiles.
C)the range.
D)the Interquartile range.

Question 52

Four students have applied to a special program and only one can be accepted.They have taken a battery of 12 tests and all have exactly the same average score.The standard deviation of their test scores are: Student A = 3.12,Student B = 0.27,Student C = 13.45,Student D = 6.45.If consistency of performance is a criteria for acceptance,which of the four students should be selected?

A)A
B)B
C)C
D)D