Deck 4: Measures of Dispersion

Question 1

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

Answer 1

4

Question 2

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

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

Answer 2

heterogeneous

Question 3

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

Answer 3

variety within the distribution of scores

Question 4

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 5

The standard deviation (s)

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 6

The distances between the scores and the mean are called

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

Question 7

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 8

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 9

Changes since 1980 show that Americans are growing more ______ in terms of race

A) similar
B) alike
C) diverse
D) predictable

Question 10

Your score on a 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 11

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 relatively easy to calculate and interpret
D) all of the above

Question 12

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

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

Question 13

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 14

The interquartile range would be an appropriate measure of dispersion for

A) nominal level variables
B) interval-ratio level variables only
C) ordinal level variables
D) skewed variables only

Question 15

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 16

Which of the following data sets shows the greatest variability?

A) 9, 10, 11
B) 0, 5, 6
C) 50, 60, 170
D) 31, 33, 35

Question 17

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

A) interval-ratio level variables
B) variables at any level of measurement
C) nominal level variables
D) ordinal level variables only

Question 18

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) non-proportional variables
C) ordinal level variables
D) skewed variables

Question 19

The second quartile (Q2) is equal in value to

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

Question 20

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 21

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 22

In the text, we examined the distribution of starting salaries for lawyers in 2012. The average salary was $81,000 but this might be misleading because the distribution

A) had a strong positive skew
B) had a strong negative skew
C) was bimodal, with few salaries close to the mean
D) had a range of only $10,000

Question 23

The text presented information about life expectancy in 40 nations. According to this information, nations at the highest income level had _______ average life expectancy and were ____ diverse.

A) higher … more
B) higher … less
C) lower … more
D) lower … less

Question 24

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

Question 25

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 26

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 27

In a boxplot, the distance from the upper to the lower "whisker" reflect the value of the

A) range
B) median
C) standard deviation
D) mean

Question 28

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 29

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 30

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 31

According to the data presented in the text, the share of income going to the lowest 20% of Americans from 1967 to 2012

A) remained virtually unchanged
B) rose dramatically
C) declined
D) rose until 1998 and then fell

Question 32

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 33

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 34

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 35

In the text, we used SPSS to compare state homicide rates in 1995 and 2012. According to the results, the average rate _____ and the distribution became _____ dispersed.

A) increased … less
B) increased … more
C) decreased … more
D) decreased … less

Question 36

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

A) index of variation
B) average deviation
C) interquartile range
D) standard deviation

Question 37

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 variation
B) average deviation
C) interquartile range
D) standard deviation

Question 38

Boxplots are graphs that display the

A) median
B) range
C) interquartile range
D) all of the above

Question 39

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