Deck 4: Measures of Variability

Question 1

Variability refers to

A) the most frequently occurring score in a distribution.
B) the most representative score in a distribution.
C) the amount of error in a distribution of scores.
D) the degree of similarity or difference in a set of scores.

Answer 1

D

Question 2

The range can be problematic as a measure of variability because it

A) only considers scores in the middle 50% of the distribution.
B) only considers the most extreme scores in the distribution.
C) only considers the high scores in the distribution.
D) only considers the low scores in the distribution.

Answer 2

B

Question 3

The high score in a distribution is 54 and the low score is 23. What is the range?

A) 30
B) 31
C) 32
D) 33

Answer 3

C

Question 4

What is the range for the following set of scores: 27, 35, 42, 47, 50?

A) 12
B) 24
C) 42
D) 23

Question 5

The interquartile range

A) is determined by considering the extreme scores in a distribution.
B) describes the range of scores from the middle 50% of the distribution.
C) only considers the high scores in a distribution.
D) only considers the low scores in a distribution.

Question 6

When dividing a distribution into four equal parts to determine the IQR, how many quartiles are produced?

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

Question 7

What is the preferred measure of variability for distributions that are skewed?

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

Question 8

An advantage of the interquartile range as a measure of variability is that it

A) is not sensitive to extreme scores.
B) takes all score values into consideration.
C) only considers the highest and lowest scores in the distribution.
D) is not influenced by the middle scores in the distribution.

Question 9

In order to determine the interquartile range, we need

A) Q₃ and Q₄.
B) Q₁ and Q₄.
C) Q₁ and Q₃.
D) Q₂ and Q₄.

Question 10

The point at or below which _________ of the scores lie is used in calculating the interquartile range.

A) 10%
B) 25%
C) 50%
D) 90%

Question 11

The point at or below which __________ of the scores lie is used in calculating the interquartile range.

A) 10%
B) 50%
C) 75%
D) 90%

Question 12

The measure of variability that does not consider values of the highest or the lowest scores is the

A) range.
B) interquartile range.
C) standard deviation.
D) median.

Question 13

What is the interquartile range for the following set of scores: 6, 8, 10, 12, 12, 12, 14, 15, 16, 16, 17, 17?

A) 5
B) 11
C) 13
D) 16

Question 14

In learning statistics, computational formulas

A) are written the way that statistics are defined.
B) guide the learner through the steps of what is being learned.
C) are easier to work with than definitional formulas.
D) involve more computations than definitional formulas.

Question 15

The computational formula for the standard deviation

A) requires the computation of deviation scores.
B) is also called the raw score formula.
C) involves more calculations that the definitional formula.
D) involves more than two columns of numbers.

Question 16

The definitional formula for the standard deviation

A) is easier to use than the computational formula.
B) requires only two columns.
C) is also called the raw score formula.
D) requires the computation of deviation scores.

Question 17

If we added up all of the deviation scores when calculating the standard deviation, the result would be equal to

A) SS.
B) 0.
C) ∑X.
D) ∑X².

Question 18

A set of scores from a population has a mean equal to 36. What is the deviation score for someone who scored 40?

A) 4
B) -4
C) 0
D) 40

Question 19

Which symbol below does not belong?

A) IQR
B) σ
C) μ
D) R

Question 20

Which of the data sets below shows the greatest amount of variability?

A) 1, 2, 3, 4
B) 6, 6, 6, 6
C) 7, 9, 11, 13
D) 2, 6, 12, 20

Question 21

Which of the following statements is true?

A) The sample mean is a biased estimate of the population mean.
B) The sample standard deviation is a biased estimate of the population standard deviation.
C) The sample standard deviation is an unbiased estimate of the population standard deviation.
D) The sample standard deviation overestimates the population standard deviation.

Question 22

The middle 50% of a normal distribution is best described by the

A) IQR.
B) R.
C) σ
D) s.

Question 23

The numerator in the formula for the standard deviation is called

A) sum of squares.
B) the variance.
C) deviation scores.
D) degrees of freedom.

Question 24

What does (X - μ) represent?

A) a standard deviation.
B) a deviation score.
C) SS.
D) the variance.

Question 25

If the standard deviation of a test was σ = 0, this would mean that

A) everyone got the same score.
B) everyone scored very low on the test.
C) everyone scored very high on the test.
D) This result is not possible.

Question 26

A set of 10 scores has a sum of squares value of 810. What is the standard deviation?

A) 8100
B) 81
C) 9
D) 90

Question 27

A set of 10 scores has a sum of squares value of 490. What is the variance?

A) 4900
B) 49
C) 7
D) 70

Question 28

A set of 10 scores has a variance of 36. What is the sum of squares?

A) 360
B) 6
C) 36
D) 60

Question 29

A set of 10 scores has a standard deviation of 4. What is the variance?

A) 1.6
B) 2.5
C) 40
D) 16

Question 30

A set of 10 scores has a standard deviation of 8. What is the sum of squares?

A) 80
B) .80
C) 640
D) 64

Question 31

Which measure of variability provides the best description of the middle 50% of the distribution?

A) the range.
B) the interquartile range.
C) the variance.
D) the standard deviation.

Question 32

The symbol σ represents

A) the sample mean.
B) the population mean.
C) the sample standard deviation.
D) the population standard deviation.

Question 33

To estimate the population standard deviation from sample data, we should use_________.

A) s
B) σ
C) σ²
D) μ

Question 34

Deviation scores are obtained by

A) subtracting the mean from the raw scores.
B) subtracting the raw scores from the mean.
C) dividing SS by N.
D) obtaining the square root of the variance.

Question 35

If we obtained the square root of the variance, the resulting value would be

A) the standard deviation.
B) the deviation score.
C) sum of squares.
D) the interquartile range.

Question 36

If we divided SS by N, the resulting value would be

A) the interquartile range.
B) the variance.
C) a deviation score.
D) the standard deviation.

Question 37

If we squared the standard deviation, the resulting value would be

A) the interquartile range.
B) a deviation score.
C) sum of squares.
D) the variance.

Question 38

If we squared the standard deviation, the resulting value would give us _________.

A) SS
B) s
C) σ²
D) σ

Question 39

If we obtained the square root of the variance, the resulting value would be __________.

A) σ
B) σ²
C) SS
D) s²

Question 40

Why is the range sometimes problematic as a measure of variability?

Question 41

For the following set of scores: 6, 12, 9, 8, 12, 7, 6, 8, 5, 12, 8, 7
a. determine the range.
b. determine the interquartile range.

Question 42

A set of 15 scores from a population has a sum of squares value of 675.
a. What is the variance?
b. What is the standard deviation?

Question 43

A set of scores from a population has a variance of 62. What is the standard deviation?

Question 44

Identify what the following symbols represent.
a. M
b. μ
c. σ²
d. σ
e. s

Question 45

The following set of scores are from a population: 1, 2, 3, 4, 5. Using the definitional formula, calculate
a. SS.
b. σ²
c. σ

Question 46

The following scores are from a sample and will be used to estimate the standard deviation for a population: 7, 4, 8, 6, 10. Using the definitional formula, calculate the standard deviation.

Question 47

The following set of scores are from a population: 5, 10, 12, 13, 6, 9. Using the computational formula, calculate
a. SS.
b. σ²
c. σ

Question 48

The following scores are from a sample and will be used to estimate the standard deviation for a population: 8, 6, 3, 9, 4. Using the computational formula, calculate the standard deviation.

Question 49

The scores from a population are as follows: 58, 41, 75, 38, 47, 56, 41, 36, 55, 39.
a. Calculate the population standard deviation.
b. Assume that you randomly drew the scores 38, 55, and 41 from that population. Calculate the sample standard deviation using the sample scores.
c. Why is the sample standard deviation usually smaller than the population standard deviation?
d. What can be done to compensate for the underestimation of the sample standard deviation?