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**Sample Questions Posted Below**

**Chapter 5: Measures of Dispersion**

**Test Bank**

- Measures that capture differences within a variable are called:
- measures of central tendency.

*b. measures of dispersion.

- summary measures.
- standard deviations.

@ Answer Location: Introduction; Cognitive Domain: Knowledge; Question Type: MC

- Which measure of dispersion is appropriate to use with nominal level variables?

*a. Variation ratio

- Range
- Variance
- Standard deviation

@ Answer Location: Measure Dispersion for Nominal and Ordinal Level Variables; Cognitive Domain: Comprehension; Question Type: MC

- What is the range for the following set of data?

1, 2, 6, 4, 10, 9, 12, 5, 9, 6, 13

- 9
- 10
- 11

*d. 12.

@ Answer Location: The Range and Interquartile Range; Cognitive Domain: Application; Question Type: MC

- The range of the middle 50% of scores in a data set is the:
- range
- variance

*c. interquartile range

- standard deviation

@ Answer Location: The Range and Interquartile Range; Cognitive Domain: Knowledge; Question Type: MC

- Calculate the interquartile range from the following set of data.

16, 92, 24, 41, 36, 91, 48, 19, 45, 88, 54, 62

- 26
- 38
- 52
- 76

@Answer Location: The Mean for Grouped Data; Cognitive Domain: Application; Question Type: MC

- The distance of a score from the mean is referred to as:
- the range.
- the variance.
- the standard deviation.

*d. the mean deviation score.

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Knowledge; Question Type: MC

- The variance is:
- the extent to which the observations are not concentrated in the modal category of the variable.
- distance of a score from the mean.

*c. the average-squared difference of each score in a set of scores from the mean of those scores.

- the square root of the average squared difference of each score in a set of scores from the mean of those scores.

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Knowledge; Question Type: MC

- What would the variance be for the following data?

10, 19, 15, 20, 21, 11

- 16.00
- 21.30

*c. 22.40

- 24.56

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Analysis; Question Type: MC

- What would the standard deviation be for the following data?

25, 27, 29, 20, 21

- 3.15

*b. 3.85

- 15
- 16.80

@Answer Location: The Standard Deviation and Variance; Cognitive Domain: Analysis; Question Type: MC

- The __________ of a distribution of scores for a variable is measured by the __________________.
- mode; symmetry
- variance; variability
- mean; modality

*d. standard deviation; variability

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Comprehension; Question Type: MC

- The variation ratio is a measure of dispersion that is appropriate to use for variables such as religion, gender, and race.

*a. True

- False

@ Answer Location: Measure Dispersion for Nominal and Ordinal Level Variables; Cognitive Domain: Application; Question Type: TF

- The simples measure of dispersion for interval level variables in the variance?
- True

*b. False

@ Answer Location: The Range and Interquartile Range; Cognitive Domain: Knowledge; Question Type: TF

- If two different sets of data have the same range, the variability for both sets has to be the same.
- True

*b. False

@ Answer Location: The Range and Interquartile Range; Cognitive Domain: Application; Question Type: TF

- The range and interquartile range use only two scores to estimate the amount of dispersion, making them more limited measures than the variance and standard deviation.

*a. True

- False

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Knowledge; Question Type: TF

- If the variance has been calculated, the researcher then only needs to take the square root of it to find the standard deviation.

*a. True

- False

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Comprehension; Question Type: TF

- The mean deviation is the most frequently used measure of dispersion for interval/ratio level variables.
- True

*b. False

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Knowledge; Question Type: TF

- The greater the magnitude of the variance, the less dispersed the data are.
- True

*b. False

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Comprehension; Question Type: TF

- Researchers prefer to report the variance instead of the standard deviation because it is easier to interpret and understand.
- True

*b. False

@ Answer Location: The Standard Deviation and Variance; Cognitive Domain: Comprehension; Question Type: TF

- When calculating the variance and standard deviation for grouped data, one would use the midpoint of the group instead of the individual case score.

*a. True

- False

@ Answer Location: Calculating the Variance and Standard Deviation with Grouped Data; Cognitive Domain: Comprehension; Question Type: TF

- Boxplots allow the researcher to illustrate the shape, central data points, and variability of a distribution.

*a. True

- False

@ Answer Location: Boxplots; Cognitive Domain: Knowledge; Question Type: TF

- Define the measures of dispersion and which type of variables can they be applied to?

*a. Answers may vary

The variation ratio is a very simple measure of dispersion that you can use whenever you have data measured at the nominal or ordinal level. The measure of dispersion for this type of data, the variation ratio, is based on the mode. The variation ratio (VR) simply measures the extent to which the observations are *not* concentrated in the modal category of the variable. More specifically, it is the proportion of cases not in the modal category of the variable.

The range is the difference between the highest score in the distribution and the lowest score:

*Range = highest value* – *lowest value.* The range can be used with interval/ratio level variables:

*The interquartile range (IQR)*. In calculating the interquartile range, we still take the difference between two scores, but rather than taking the difference between the highest and lowest scores, in the IQR we take the difference between the score at the 75th percentile (the third quartile or Q_{3}) and the score at the 25th percentile (the first quartile or Q_{1}). Note that since we are taking the range of scores between the 75th and 25th percentiles, this range covers the dispersion at the middle 50 percent of our distribution. In other words, one-half of all our scores can be found between the 75th and 25th percentiles and the IQR measures the dispersion within those two boundaries.

The variance is the average squared difference of each score in a set of scores from the mean of those scores.

The variance is the standard deviation squared while the standard deviation is the square root of the variance. The standard deviation standardizes the scores so that they are easier to interpret and are comparable across groups. The variance and standard deviation are the two most frequently used measures of dispersion for interval/ratio-level data.

@Answer Location: The Variation Ratio, The Range and Interquartile Range, The Standard Deviation and Variance; Cognitive Domain: Application; Question Type: SA

- Calculate the Variation Ratio for the following data.

__Type of Offender f __

Non-offender 5000

One-Time 600

Recidivist 350

Chronic 150

*Proportion for the modal category is .82; 1 – .82 = .18; 18 percent of cases not in the modal category

@Answer Location: The Variation Ratio; Cognitive Domain: Application; Question Type: SA

- Calculate the range and the interquartile range from the following data. Why is there a difference between the two?

10, 27, 28, 20, 30, 43, 55, 13, 24, 19, 40, 43

**Range* = 55 -10 =45

*Interquartile range* = 20

The range is much larger than the interquartile range because the interquartile range is less influenced by outliers.

@Answer Location: The Range and Interquartile Range; Cognitive Domain: Application; Question Type: SA

- Calculate the range, variance and standard deviation from the following data.

10, 20, 30, 35, 25, 50

**Range* = 40; *Variance* = 177.77; *Standard deviation* = 13.33

@Answer Location: The Standard Deviation and Variance; Cognitive Domain: Application; Question Type: SA

- Calculate the variance and standard deviation from the following data.

*X* *X ^{2}*

10

15

14

19

9

∑ ∑

**Variance* = 13.27; *Standard deviation* = 3.64

@Answer Location: Computational Formulas for Variance and Standard Deviation; Cognitive Domain: Application; Question Type: SA

Category: Statistics

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