Measures of Dispersion: Understanding Data Spread in Statistics

Question 1

The standard deviation of a dataset is 5. What is the variance of the same dataset?

Accepted Answer

25

Answer

5

Answer

10

Answer

50

Question 2

Which of the following datasets has the largest range?

Accepted Answer

{1, 2, 20, 50, 100}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 2, 3, 10, 11}

Answer

{1, 2, 10, 20, 30}

Question 3

Which of the following datasets has the smallest variance?

Accepted Answer

{1, 1, 1, 1, 1}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 3, 5, 7, 9}

Answer

{1, 5, 10, 15, 20}

Question 4

Which of the following measures of dispersion is the least affected by outliers?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 5

A dataset has a range of 20. What does this indicate about the spread of the data?

Accepted Answer

The data is widely dispersed.

Answer

The data is moderately dispersed.

Answer

The data is clustered closely around the mean.

Answer

The range provides no information about the spread of the data.

Question 6

Which of the following is NOT a measure of dispersion used to understand the spread and variability of data?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Interquartile range

Question 7

The variance of a data set is 100. What is its standard deviation?

Accepted Answer

20

Answer

10

Answer

30

Answer

40

Question 8

Which measure of dispersion is most appropriate for data that is not normally distributed?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 9

Which of the following statements about the interquartile range is accurate?

Accepted Answer

It represents the difference between the 25th and 75th percentiles.

Answer

It is not affected by outliers.

Answer

It can have negative values.

Answer

It is always larger than the range.

Question 10

Which measure of dispersion represents the average squared difference between data points and their mean?

Accepted Answer

Variance

Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Question 11

How do you calculate the interquartile range?

Accepted Answer

Subtract the first quartile from the third quartile

Answer

Subtract the second quartile from the first quartile

Answer

Subtract the mean from the median

Answer

Add the first and third quartiles

Question 12

Which of these is not a measure of dispersion?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 13

If data points in a dataset are multiplied by 2, what happens to the standard deviation?

Accepted Answer

Doubles

Answer

Decreases by half

Answer

Remains the same

Answer

Quadruples

Question 14

Which measure of dispersion is a non-parametric statistic?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 15

Which of the following best describes measures of dispersion?

Accepted Answer

Numerical values that quantify the spread or variability of data

Answer

Measures that describe the central tendency of data

Answer

Qualitative indicators of data distribution

Question 16

What is the range of a dataset that has a minimum value of 10 and a maximum value of 30?

Accepted Answer

20

Answer

15

Answer

25

Question 17

Which measure of dispersion focuses on the middle 50% of a dataset?

Accepted Answer

Interquartile range (IQR)

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 18

A dataset with a standard deviation of 15 is considered:

Accepted Answer

More dispersed or spread out

Answer

Less dispersed or clustered

Answer

Symmetrically distributed

Question 19

For approximately normally distributed data, which measure of dispersion is generally preferred?

Accepted Answer

Standard deviation

Answer

Interquartile range

Answer

Range

Question 20

When analyzing a dataset with a skewed distribution, which measure of dispersion is most appropriate?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Question 21

A researcher wants to determine the variability of cholesterol levels in a patient group. Which measure of dispersion is most suitable for this purpose?

Accepted Answer

Standard Deviation

Answer

Median

Answer

Mode

Answer

Mean

Question 22

The difference between the highest and lowest values in a dataset is called the:

Accepted Answer

Range

Answer

Interquartile Range

Answer

Variance

Answer

Standard Deviation

Question 23

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Standard Deviation

Answer

Variance

Answer

Interquartile Range

Question 24

A dataset has a standard deviation of 5. This indicates that:

Accepted Answer

The data points typically deviate by 5 units from the mean.

Answer

The data points are all exactly 5 units apart.

Answer

The average data point is 5.

Question 25

A dataset with a small standard deviation suggests that:

Accepted Answer

The data points are closely clustered around the mean.

Answer

The data points are spread out over a wide range.

Answer

The mean is very high.

Question 26

Which measure of dispersion is most appropriate for describing the spread of data in a skewed distribution?

Accepted Answer

Interquartile Range

Answer

Standard Deviation

Answer

Range