Measures of Variability: Quantifying Data Spread in Statistics for Psychology

Question 1

A data set with a smaller range is less variable than a data set with a larger range.

Accepted Answer

True

Answer

False

Question 2

A data set with a higher standard deviation is more spread out than a data set with a lower standard deviation.

Accepted Answer

True

Answer

False

Question 3

Which of the following is not a characteristic of variance?

Accepted Answer

It is a measure of central tendency

Answer

It is always positive

Answer

It is expressed in squared units

Answer

It is calculated from the square root of standard deviation

Question 4

A dataset with a large standard deviation is considered:

Accepted Answer

Highly variable

Answer

Moderately variable

Answer

Slightly variable

Answer

Not variable

Question 5

A distribution with a standard deviation of 0 indicates it is:

Accepted Answer

Uniformly distributed

Answer

Normally distributed

Answer

Skewed

Answer

Bimodal

Question 6

Which measure of variability is least affected by outliers?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 7

Which measure of variability divides a data set into four equal parts, with the 25th percentile representing the lower quartile and the 75th percentile representing the upper quartile?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 8

Which measure of variability is most heavily influenced by outliers and extreme values?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 9

Which measure of variability is most appropriate for describing the spread of data that is not normally distributed?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 10

Which measure of variability is a standardized score that allows for comparison of data sets with different means and standard deviations?

Accepted Answer

z-score

Answer

t-score

Answer

F-score

Answer

p-score

Question 11

Which measure of variability quantifies the difference between the maximum and minimum values in a data set?

Accepted Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Answer

Variance

Question 12

The Interquartile Range (IQR) represents the variability of which portion of the data set?

Accepted Answer

Middle 50%

Answer

Middle 25%

Answer

Top 25%

Answer

Bottom 25%

Question 13

Which measure of variability represents the average distance of data points from the mean?

Accepted Answer

Standard Deviation

Answer

Range

Answer

Interquartile Range

Answer

Variance

Question 14

Which measure of variability is most affected by extreme values?

Accepted Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Answer

Variance

Question 15

In a normal distribution, the standard deviation is always:

Accepted Answer

Positive

Answer

Zero

Answer

Negative

Answer

Positive or negative

Question 16

Which of the following is NOT an application of measures of variability in psychology?

Accepted Answer

Predicting the weather

Answer

Describing the variability of test scores

Answer

Identifying outliers in data

Answer

Comparing the effectiveness of different treatments

Question 17

A data set has an Interquartile Range of 8. What does this value represent?

Accepted Answer

The middle 50% of data points have a spread of 8

Answer

The middle 25% of data points have a spread of 8

Answer

The top 25% of data points have a spread of 8

Answer

The bottom 25% of data points have a spread of 8

Question 18

Which measure of variability quantifies the range or spread of a data set by calculating the difference between the maximum and minimum values?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 19

Which measure of variability represents the average of the squared differences between each data point and the mean?

Accepted Answer

Variance

Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Question 20

Which measure of variability is most sensitive to extreme data values?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 21

A data set has a mean of 60 and a standard deviation of 12. Approximately what percentage of data points lie within one standard deviation of the mean?

Accepted Answer

68%

Answer

34%

Answer

95%

Answer

99%

Question 22

What is a potential drawback of using standard deviation as a measure of variability?

Accepted Answer

It can be influenced by extreme values (outliers).

Answer

It is widely used and easy to understand.

Answer

It does not have units.

Answer

It can be directly interpreted from the original data.

Question 23

How does the choice of variability measure affect the interpretation of statistical results?

Accepted Answer

Different variability measures provide unique insights into data spread, influencing the conclusions drawn from statistical analyses.

Answer

The choice of variability measure has no significant impact on the interpretation of statistical results.

Answer

Variability measures are primarily descriptive tools with limited relevance to statistical inference.

Answer

The interpretation of variability measures is always straightforward and unambiguous.

Question 24

The variance is mathematically equivalent to the square of the:

Accepted Answer

Standard deviation

Answer

Mean

Answer

Interquartile range

Answer

Range

Question 25

Data with a high standard deviation indicates that:

Accepted Answer

Data points are widely dispersed from the mean.

Answer

Values are closely clustered around the mean.

Answer

The distribution is skewed.

Answer

The data set is normally distributed.

Question 26

Which of the following is NOT a measure of variability?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Interquartile range

Question 27

Data that follows a normal distribution typically has a:

Accepted Answer

Bell-shaped curve

Answer

Skewed curve

Answer

Bimodal curve

Answer

No discernible pattern

Question 28

In which scenario would it be most appropriate to use a large standard deviation as a measure of variability?

Accepted Answer

Test scores from a challenging exam

Answer

Ages of people in a retirement community

Answer

Weights of newborn infants

Answer

Years of experience of employees in a corporation

Question 29

Which of the following measures of variability represents the difference between the highest and lowest values in a data set?

Accepted Answer

Range

Answer

Standard deviation

Answer

Interquartile range

Question 30

Which measure of variability is most sensitive to outliers?

Accepted Answer

Range

Answer

Interquartile range

Answer

Variance

Answer

Standard deviation

Question 31

Which of the following is NOT a property of standard deviation?

Accepted Answer

It can take on negative values.

Answer

It measures the average distance from the mean.

Answer

It is always positive.

Answer

It is a unit-less measure.

Question 32

Which of the following data sets has the greatest variability?

Accepted Answer

1, 3, 5, 7, 9

Answer

1, 1, 1, 1, 1

Answer

0, 2, 4, 6, 8

Answer

2, 4, 6, 8, 10

Question 33

Which measure of variability describes the difference between the largest and smallest values in a data set?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Question 34

What measure of variability represents half the distance between Q3 and Q1?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 35

Which measure of variability is a commonly used absolute measure of dispersion that signifies how far each data point is from the mean?

Accepted Answer

Standard deviation

Answer

Interquartile range

Answer

Variance

Answer

Range

Question 36

What is the relationship between variance and standard deviation?

Accepted Answer

Variance is the square of standard deviation

Answer

Standard deviation is the square of variance

Answer

Variance is the average of standard deviation

Answer

Standard deviation is the average of variance

Question 37

Which of the following is NOT a factor that affects the measure of variability?

Accepted Answer

Sample size

Answer

Outliers

Answer

Central tendency

Answer

Data distribution

Question 38

In a data set with a large range, what conclusion can be drawn?

Accepted Answer

The data has high variability

Answer

The data has low variability

Answer

The mean of the data is high

Answer

The median of the data is low

Question 39

Which measure of variability is most resistant to outliers?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Range

Answer

Variance

Question 40

What is the standard deviation of a data set with only one value?

Accepted Answer

0

Answer

Cannot be determined

Answer

The mean of the data

Answer

1

Question 41

Which of the following is true about the variance of a random variable?

Accepted Answer

It cannot be negative

Answer

It is always greater than the standard deviation

Answer

It can be negative

Answer

It is always less than the standard deviation

Question 42

In a normal distribution, approximately what percentage of data points falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

50%

Answer

75%

Answer

95%