Measures of Dispersion: Understanding Data Spread in Statistics

Question 1

Which of the following is NOT an application of measures of dispersion?

Accepted Answer

Making predictions about future data points

Answer

Identifying outliers

Answer

Comparing variability across different datasets

Answer

Describing the distribution of a dataset

Question 2

For a skewed dataset, the most appropriate measure of dispersion is:

Accepted Answer

Interquartile range

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 3

Which measure of dispersion indicates how spread out a dataset is relative to its mean?

Accepted Answer

Standard deviation

Answer

Range

Answer

Variance

Answer

Median

Question 4

How is variance related to standard deviation?

Accepted Answer

Variance is the square of the standard deviation

Answer

Standard deviation is the square of the variance

Answer

Variance and standard deviation represent the same measure

Answer

Standard deviation is the reciprocal of the variance

Question 5

A dataset with a standard deviation of 0 implies that:

Accepted Answer

All data points are identical.

Answer

The data is necessarily normally distributed.

Answer

The data is skewed to the left.

Answer

The data has multiple modes.

Question 6

Which of the following properties applies to standard deviation?

Accepted Answer

It is always nonnegative

Answer

It can take negative values

Answer

It is always larger than the range

Answer

It is always smaller than the range

Question 7

If the standard deviation of a dataset is 10, what is the variance?

Accepted Answer

100

Answer

10

Answer

20

Answer

5

Question 8

The range of a dataset is calculated as the difference between:

Accepted Answer

The largest and smallest values

Answer

The mean and median

Answer

The variance and standard deviation

Answer

The first and third quartiles

Question 9

The standard deviation of a dataset is always:

Accepted Answer

Greater than or equal to zero

Answer

Less than or equal to the range

Answer

Between the mean and the median

Answer

Equal to the variance

Question 10

One advantage of using standard deviation as a measure of dispersion is that it:

Accepted Answer

Is based on all the data points in the dataset

Answer

Is not affected by outliers

Answer

Is easy to calculate

Answer

Can be negative

Question 11

Which measure of dispersion is influenced significantly by extreme values (outliers)?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Mean

Question 12

The variance of a dataset is mathematically equivalent to the square of its:

Accepted Answer

Standard deviation

Answer

Mean

Answer

Range

Answer

Median

Question 13

Which measure of dispersion remains unaffected by the presence of extreme values (outliers)?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 14

A dataset has a mean of 50 and a standard deviation of 10. What is the coefficient of variation (CV)?

Accepted Answer

20%

Answer

10%

Answer

5%

Answer

50%

Question 15

Two datasets have the same mean. What can we conclude about their standard deviations?

Accepted Answer

They could be different.

Answer

They must be the same.

Answer

They must be different.

Answer

None of the above.

Question 16

A company wants to compare the variability of sales figures across two regions. Which measure of dispersion would be most suitable?

Accepted Answer

Standard deviation

Answer

Interquartile range

Answer

Coefficient of variation

Answer

Range

Question 17

A dataset has a standard deviation of 0. What does this imply?

Accepted Answer

All data points are identical.

Answer

There are no outliers.

Answer

The data is normally distributed.

Question 18

The interquartile range (IQR) measures the dispersion of which part of the data?

Accepted Answer

The middle 50% of the data

Answer

The lower 25% of the data

Answer

All data points

Answer

The upper 25% of the data

Question 19

Which measure of dispersion is most appropriate for comparing the variability of two datasets with different means?

Accepted Answer

Coefficient of variation

Answer

Standard deviation

Answer

Range

Answer

Variance

Question 20

A researcher is studying the distribution of heights in a sample of students. Which measure of dispersion would be most helpful in understanding the spread of heights around the average height?

Accepted Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Answer

Variance

Question 21

Which measure of dispersion is most sensitive to extreme values?

Accepted Answer

Range

Answer

Variance

Answer

Interquartile Range

Answer

Standard Deviation

Question 22

A dataset has a standard deviation of 0. What can you conclude about the data?

Accepted Answer

All data points are identical.

Answer

The mean is zero.

Answer

The data is normally distributed.

Answer

The data is skewed.

Question 23

The interquartile range (IQR) represents the spread of the data between which percentiles?

Accepted Answer

25th and 75th

Answer

5th and 95th

Answer

1st and 99th

Answer

10th and 90th

Question 24

You are analyzing the heights of students in two different classes. Class A has a smaller variance than Class B. What can you conclude about the heights of students in each class?

Accepted Answer

The heights of students in Class A are more similar to each other than the heights of students in Class B.

Answer

Class A has a higher average height than Class B.

Question 25

A company wants to compare the variability of the prices of its products in two different regions. Which measure of dispersion would be most appropriate?

Accepted Answer

Coefficient of Variation

Answer

Standard Deviation

Answer

Interquartile Range

Answer

Range

Question 26

Given a dataset with a mean of 50 and a standard deviation of 10, what is the range within which approximately 68% of the data points would fall?

Accepted Answer

40 to 60

Answer

30 to 70

Answer

10 to 90

Answer

20 to 80

Question 27

What is the main advantage of using the interquartile range over the range as a measure of dispersion?

Accepted Answer

It is less sensitive to extreme values.

Answer

It is easier to calculate.

Answer

It provides more information about the distribution.

Question 28

Two datasets have the same mean but different variances. Which dataset will have a wider spread?

Accepted Answer

The dataset with the higher variance.

Answer

It is impossible to determine without more information.

Answer

They will have the same spread.

Answer

The dataset with the lower variance.

Question 29

You are analyzing the performance of two different investment strategies. Strategy A has a higher standard deviation than Strategy B. What can you conclude about the risk associated with each strategy?

Accepted Answer

Strategy A is riskier than Strategy B.

Answer

Strategy B is riskier than Strategy A.

Answer

Both strategies have the same level of risk.

Answer

It is impossible to determine without more information.