Deck 4: Measures of Variation

Question 1

The range is:

A) the arithmetic average.
B) the middle score in a distribution after the scores have been ordered from highest to lowest or
Lowest to highest.
C) the average difference between the scores in a distribution and the mean of the distribution.
D) the difference between the lowest and highest score in a distribution.

Answer 1

the difference between the lowest and highest score in a distribution.

Question 2

The standard deviation is:

A) the arithmetic average.
B) the middle score in a distribution after the scores have been ordered from highest to lowest or
Lowest to highest.
C) the square root of the average squared deviation from the mean.
D) the difference between the lowest and highest score in a distribution.

Answer 2

the square root of the average squared deviation from the mean.

Question 3

The average deviation is:

A) the arithmetic average.
B) the average distance between the scores in a distribution and the mean of the distribution.
C) the square root of the average squared deviation from the mean.
D) the difference between the lowest and highest score in a distribution.

Answer 3

the average distance between the scores in a distribution and the mean of the distribution.

Question 4

When we square the deviation scores while calculating a measure of variability, we are using the _____.

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

Question 5

When we take the absolute value of the deviation scores while calculating a measure of variability, we are using the _____.

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

Question 6

When calculated on the same distribution of scores, the average deviation will be _____ the standard deviation.

A) less than
B) greater than
C) the same as
D) either greater than or the same as

Question 7

The symbol $\sigma$ represents the standard deviation for _____.

A) a sample
B) the unbiased estimator of the population standard deviation
C) a population
D) none of the above

Question 8

The symbol S represents the standard deviation for _____.

A) a sample
B) the unbiased estimator of the population standard deviation
C) a population
D) none of the above

Question 9

The symbol s represents the standard deviation for _____.

A) a sample
B) the unbiased estimator of the population standard deviation
C) a population
D) none of the above

Question 10

When calculating the unbiased estimator of the population standard deviation, we divide by _____ rather than _____ as we do with either $\sigma$ or S.

A) N - 2; N
B) N - 1; N
C) N; N - 1
D) N - 2; N - 1

Question 11

When calculating $\sigma$ or S, we divide by _____ rather than _____ as we do with the unbiased estimator of the standard deviation.

A) N - 2; N
B) N - 1; N
C) N; N - 1
D) N - 2; N - 1

Question 12

When calculated on the same distribution of scores, the unbiased estimator of the standard deviation will be _____ $\sigma$ .

A) greater than
B) less than
C) the same as
D) either greater than or the same as

Question 13

Which of the following is a disadvantage of using the range as a measure of variation?

A) It is limited because only two of the scores in a distribution are used to derive it.
B) It is easily distorted by an unusually high or low score in a distribution.
C) It can only be used with nominal data.
D) Both a and b are disadvantages.

Question 14

The calculation of the average deviation differs from the calculation of the standard deviation in that the deviation scores:

A) are squared.
B) are converted to absolute values.
C) are squared and converted to absolute values.
D) do not differ.

Question 15

Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _____ standard deviation and a _____ average deviation in comparison to distribution B.

A) larger; larger
B) smaller; smaller
C) larger; smaller
D) smaller; larger

Question 16

Which of the following is NOT TRUE?

A) The range is a simplistic measure of variation that does not use all scores in a distribution
In its calculation.
B) When compared with the range, the average deviation is a more sophisticated measure of variation in which all scores are used, but which may not weight extreme scores adequately.
C) The standard deviation is the least sophisticated measure of variation and the least
Frequently used.
D) All of the above.

Question 17

If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the left than to the right, how would the distribution be skewed?

A) Normally
B) Negatively
C) Positively
D) Average

Question 18

In a negatively skewed distribution, the mean is _____ the median and _____ the mode.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than

Question 19

In a negatively skewed distribution, the mode is _____ the median and _____ the mean.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than

Question 20

In a negatively skewed distribution, the median is _____ the mode and _____ the mean.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than

Question 21

In a positively skewed distribution, the mean is _____ the median and _____ the mode.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than

Question 22

In a positively skewed distribution, the mode is _____ the median and _____ the mean.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than

Question 23

In a positively skewed distribution, the median is _____ the mean and _____ the mode.

A) greater than; greater than
B) less than; less than
C) greater than; less than
D) less than; greater than