Deck 5: Looking at Data: Measures of Variability

Question 1

The sum of the squared differences of each score from the mean of a distribution divided by the number of scores is the definition for the.

A)estimated population standard deviation
B)estimated population variance
C)sample variance
D)sample standard deviation

Answer 1

C

Question 2

Which of the following sets of scores has the largest estimated population variance?

A)3, 3, 3, 3, 3
B)1, 2, 3, 4, 5
C)2, 2, 3, 4, 4
D)1, 1, 3, 5, 5

Answer 2

D

Question 3

The sample variance is defined as the sum of the.

A)squared differences of each score from the mean of a distribution divided by the sample size
B)differences of each score from the mean of a distribution divided by the sample size
C)squared differences of each score from the mean of a distribution divided by the sample size minus one
D)differences of each score from the mean of a distribution divided by the sample size minus one

Answer 3

A

Question 4

The range for the scores 10, 11, 12, 14, 16, 16, 16, 18, 19, 20 is.

A)11
B)10
C)16
D)5

Question 5

The estimated population variance is defined as the sum of the.

A)squared differences of each score from the mean of a distribution divided by the sample size
B)differences of each score from the mean of a distribution divided by the sample size
C)squared differences of each score from the mean of a distribution divided by the sample size minus one
D)differences of each score from the mean of a distribution divided by the sample size minus one

Question 6

The numerator in the formula for calculating a variance is called a.

A)sum of squares
B)differences squared
C)squared sums
D)squared differences

Question 7

Which of the following is the formula for the estimated population variance?

Question 8

The scores cluster around a measure of central tendency in a distribution, the that measure of central tendency represents the scores.

A)less; better
B)more; less
C)more; better
D)none of the above

Question 9

The range is the.

A)difference between the highest and the lowest score in a distribution
B)sum of the highest and lowest scores divided by two in a distribution
C)difference between the 25th and the 75th percentiles in a distribution
D)interval that contains the middle 50 percent of the scores in a distribution

Question 10

Which of the following sets of scores has the largest range?

A)1, 1, 1, 4, 7, 7, 7
B)2, 2, 3, 4, 5, 6, 6
C)3, 3, 3, 4, 5, 5, 5
D)4, 4, 4, 4, 4, 4, 4

Question 11

The sum of the squared deviations from a population mean divided by the population size is the definition for the.

A)population standard deviation
B)population variance
C)sample variance
D)sample standard deviation

Question 12

The term refers to how much scores in a distribution differ from each other.

A)modality
B)variability
C)stability
D)similarity

Question 13

Which of the following is the formula for the variance of a sample used to estimate the population variance?

Question 14

The dispersion there is among scores in a distribution, the the mean depicts a typical score for that distribution.

A)more; better
B)more; less
C)less; less
D)greater; better

Question 15

Which of the following is the formula for the population variance?

Question 16

The sum of the squared deviations from the mean divided by the number of scores minus one is the definition for the.

A)estimated population standard deviation
B)estimated population variance
C)sample variance
D)sample standard deviation

Question 17

The estimated population variance is represented by.

A)s
B)
C)
D)

Question 18

The population variance is represented by.

Question 19

A measure of central tendency of a distribution is most representative of individual scores when there is variability among the scores.

A)little
B)moderate
C)much
D)normal

Question 20

The population variance is defined as the sum of the.

A)squared differences of each score from the sample mean of a distribution divided by the sample size
B)differences of each score from the mean of a population divided by the population size
C)squared differences of each score from the mean of a population divided by the population size
D)differences of each score from the mean of a population divided by the population size minus one

Question 21

The population standard deviation is represented by.

A)
B)
C)S
D)s

Question 22

If a variance for a set of scores is 25.0, then the standard deviation for those scores is.

A)2.5
B)5.0
C)10.0
D)cannot determine from

Question 23

If the SS for a set of scores is zero, then s for those scores is.

A)zero
B)+1.0
C)-1.0
D)cannot determine from the

Question 24

The sample mean predicts every score in a distribution perfectly when.

A)s = 0
B)s2 = 0
C)SS = 0
D)all the above

Question 25

A SS is given by.

Question 26

The sample mean predicts every score in a distribution perfectly when.

A)s = 1
B)s = 0
C)s2 = 1
D)SS = 1

Question 27

The estimated population standard deviation is defined as the.

A)estimated population variance divided by the size of the sample
B)square root of the estimated population variance
C)estimated population variance divided by the size of the sample minus one
D)estimated population variance squared

Question 28

represents the formula for the.

A)sample variance
B)estimated population variance
C)sample standard deviation
D)estimated population standard deviation

Question 29

The square root of the estimated population variance is the estimated population.

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

Question 30

The estimated population standard deviation of the scores 2, 4, 6 is.

A)0.67
B)1.00
C)2.00
D)4.00

Question 31

If all the scores in a distribution are the same value, then the estimated population variance of the scores will be.

A)1.0
B)equal to the mean of the set
C)zero
D)cannot determine without knowing the number of scores in the set

Question 32

The population standard deviation is defined as the.

A)population variance divided by the size of the population
B)population variance divided by the size of the population minus one
C)square root of the population variance
D)population variance squared

Question 33

If a standard deviation for a set of scores is 4.0, then the variance for those scores is.

A)2.0
B)4.0
C)8.0
D)none of the above

Question 34

The addition of an extreme value to a set of scores.

A)leaves the value of SS unchanged
B)decreases the range
C)decreases the standard deviation
D)increases the variance

Question 35

The estimated population standard deviation will be equal to zero when.

A)a distribution is normal
B)the mean, median and mode all have the same value
C)all the scores in a distribution have the same value
D)a distribution is unimodal and symmetrical

Question 36

The square root of the population variance is the population.

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

Question 37

Which of the following sets of scores has the smallest value of s?

A)1, 1, 1, 4, 7, 7, 7
B)1, 2, 3, 4, 5, 6, 7
C)7, 7, 7, 7, 7, 7, 7
D)1, 1, 1, 2, 3, 3, 3

Question 38

The square root of the variance is the.

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

Question 39

The estimated population variance of the scores 2, 4, 6 is.

A)0.67
B)1.00
C)2.00
D)4.00

Question 40

The estimated population standard deviation is represented by.

A)s

Question 41

The mean and standard deviation are the preferred descriptive statistics when a frequency distribution is.

A)unimodal and symmetrical
B)bimodal and skewed
C)positively or negatively skewed
D)any of the above

Question 42

Which of the following scales of measurement ordinarily does not lend itself to a measure of variability?

A)Nominal
B)Ordinal
C)Interval
D)Ratio

Question 43

If a distribution of scores is approximately symmetrical, then the and are the preferred descriptive statistics.

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

Question 44

The symbol typically used for journal article presentations of the standard deviation is .

A)s
B)S
C)SD

Question 45

If a standard deviation for a set of scores is 9.0, then the variance for those scores is.

A)81.0
B)18.0
C)9.0
D)3.0

Question 46

If the SS for a set of scores is 100 and the sample size is 51, then s for those scores is.

Question 47

When the measure of central tendency is the median, which of the following is an appropriate measure of variability?

A)Variance
B)Standard deviation
C)Range
D)All the above

Question 48

The choice of a measure of variability to describe scores is determined by which of the following?

A)The scale of measurement.
B)The shape of the frequency distribution.
C)The intended further statistical analysis of the data.
D)All the above.

Question 49

The choice of a measure of variability to describe scores is not determined by which of the following?

A)The scale of measurement.
B)The size of the class interval.
C)The shape of the frequency distribution.
D)The intended further statistical analysis of the data.

Question 50

Which of the following measures of variability includes 100 percent of the scores in a distribution?

A)range
B)variance
C)parameter
D)standard deviation

Question 51

When scores represent ratio level of the measurement, the is the preferred measure of central tendency and the the preferred measure of variability.

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

Question 52

Which of the following measures of variability does not make use all the scores in a distribution for its computation?

A)Population standard deviation
B)Estimated population standard deviation
C)Estimated population variance
D)Range

Question 53

If the appropriate measure of central tendency is the mean, then the most appropriate measure of variability is the.

A)median
B)range
C)standard deviation
D)population variance