Measures of Dispersion: Master Data Spread in Statistics

Question 1

What is the interquartile range (IQR) of the following dataset: 10, 12, 14, 16, 18, 20, 22, 24, 26, 28?

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Question 2

The standard deviation is primarily a measure of:

Accepted Answer

Dispersion

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 3

Which measure of dispersion is most sensitive to outliers in a dataset?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 4

The coefficient of variation measures:

Accepted Answer

Relative dispersion

Answer

Absolute dispersion

Answer

Central tendency

Answer

Skewness

Question 5

Which measure of dispersion is the square of the standard deviation?

Accepted Answer

Variance

Answer

Range

Answer

Interquartile range

Answer

Coefficient of variation

Question 6

Which measure of dispersion is expressed as a percentage?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Interquartile range

Answer

Variance

Question 7

Which measure of dispersion quantifies the average distance of data points from the mean?

Accepted Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Answer

Variance

Question 8

A data set with a greater range compared to another data set indicates:

Accepted Answer

Greater spread of data

Answer

Lower spread of data

Answer

Equal spread of data

Answer

Cannot be determined based on range alone

Question 9

Which formula calculates the sample variance of a data set?

Accepted Answer

Sum of squared deviations from the mean / (n-1)

Answer

(Maximum - Minimum)

Answer

Upper Quartile - Lower Quartile

Answer

Mean - Median

Question 10

If the standard deviation of a data set is 10 and the mean is 50, what is the z-score of a value that is 65?

Accepted Answer

1.5

Answer

1

Answer

2

Answer

2.5

Question 11

Compare the strengths and weaknesses of range, interquartile range, and standard deviation as measures of dispersion. Explain when each measure is most suitable.

Accepted Answer

Range: Easy to calculate, but influenced by outliers

Accepted Answer

Interquartile range: Less affected by outliers, suitable for skewed data

Accepted Answer

Standard deviation: Provides comprehensive information, but sensitive to outliers

Answer

All measures have similar advantages and drawbacks

Question 12

Interquartile range is a measure of dispersion that describes the spread of the:

Accepted Answer

Middle 50% of the data

Answer

Lowest 25% of the data

Answer

Highest 25% of the data

Answer

Extreme values of the data

Question 13

The coefficient of variation is a measure of dispersion that is particularly useful when comparing:

Accepted Answer

Data sets with different units of measurement

Answer

Data sets with different central tendencies

Answer

Data sets with different sample sizes

Answer

Data sets with different shapes

Question 14

Variance, often used to measure dispersion, is defined as the:

Accepted Answer

Sum of squared deviations from the mean divided by N

Answer

Square of the standard deviation

Answer

Range divided by the mean

Answer

Difference between the maximum and minimum values

Question 15

When comparing the dispersion of two data sets with different units of measurement, which measure of dispersion is most suitable?

Accepted Answer

Coefficient of variation

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 16

Which of the following is NOT an important feature or use of measures of dispersion?

Accepted Answer

Identifying the central tendency of data

Answer

Describing the spread of data

Answer

Summarizing the variability of data

Answer

Making inferences about the population

Question 17

The interquartile range (IQR) is calculated as the difference between which two quartiles?

Accepted Answer

Q1 and Q3

Answer

Q1 and Q4

Answer

Q2 and Q3

Answer

Q2 and Q4

Question 18

Which measure of dispersion is computed as the square root of the average squared deviations from the mean?

Accepted Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Answer

Variance

Question 19

The relationship between variance and standard deviation is expressed as:

Accepted Answer

Variance = Standard deviation ^ 2

Answer

Variance = Standard deviation

Answer

Variance = Standard deviation / 2

Answer

Variance = Standard deviation - 1

Question 20

Which of the following indicates a greater degree of data spread or variability?

Accepted Answer

Larger variance

Answer

Smaller IQR

Answer

Smaller coefficient of variation

Answer

Lower range

Question 21

In a positively skewed distribution, the relationship between the mean and median is:

Accepted Answer

Mean is greater than the median

Answer

Mean is less than the median

Answer

Mean is equal to the median

Answer

Relationship cannot be determined from the given information

Question 22

Which of the following is not a typical application of measures of dispersion?

Accepted Answer

Forecasting future values

Answer

Identifying outliers

Answer

Determining the spread of data

Answer

Making comparisons between data sets

Question 23

The standard deviation of a normal distribution is:

Accepted Answer

Always a positive value

Answer

Always zero

Answer

Always a negative value

Answer

Dependent on the mean of the distribution

Question 24

Which measure of dispersion quantifies the difference between the maximum and minimum values in a dataset?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 25

What is the mathematical formula for calculating the interquartile range (IQR) of a dataset?

Accepted Answer

IQR = (Q3 - Q1) / 2

Answer

IQR = Q3 - Q1

Answer

IQR = (Q3 + Q1) / 2

Answer

IQR = Q3 / Q1

Question 26

Which measure of dispersion represents the square root of the variance?

Accepted Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Answer

Variance

Question 27

What is the key difference between variance and standard deviation?

Accepted Answer

Standard deviation is the square root of the variance

Answer

Variance is squared standard deviation

Answer

Standard deviation is squared variance

Answer

Variance is the average of the squared deviations from the mean

Question 28

Which measure of dispersion is most appropriate for a dataset that exhibits a skewed distribution?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Coefficient of variation

Question 29

Which measure of dispersion quantifies the difference between the highest and lowest values in a dataset?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 30

The interquartile range (IQR) is calculated as the difference between the:

Accepted Answer

Upper quartile and lower quartile

Answer

Mean and median

Answer

Maximum and minimum values

Answer

Variance and standard deviation

Question 31

The variance of a dataset is defined as:

Accepted Answer

The square root of the average of the squared differences from the mean

Answer

The absolute value of the average of the differences from the mean

Answer

The sum of the squared differences from the median

Answer

The difference between the mean and the mode

Question 32

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

Accepted Answer

It is a measure of central tendency

Answer

It is always positive

Answer

It is measured in the same units as the original data

Answer

It allows for comparison of variability across different datasets

Question 33

A dataset with a low standard deviation indicates that the data:

Accepted Answer

Is clustered closely around the mean

Answer

Is widely dispersed

Answer

Is normally distributed

Answer

Cannot be further analyzed

Question 34

The standard deviation of a dataset can be calculated from its:

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Coefficient of variation

Question 35

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

Accepted Answer

Range

Answer

Standard deviation

Answer

Variance

Answer

Interquartile range

Question 36

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mode

Answer

Standard deviation

Answer

Variance

Answer

Interquartile range

Question 37

The interquartile range (IQR) represents:

Accepted Answer

The difference between the upper and lower quartiles

Answer

The distance between the smallest and largest data points

Answer

The average of the quartiles

Answer

The difference between the median and the upper quartile

Question 38

Which measure of dispersion is the square root of the variance?

Accepted Answer

Standard deviation

Answer

Range

Answer

Interquartile range

Answer

Coefficient of variation

Question 39

A sample has a mean of 10 and a standard deviation of 5. Which of the following intervals contains approximately 68% of the data, according to the empirical rule?

Accepted Answer

[7.5, 12.5]

Answer

[5, 15]

Answer

[9, 11]

Answer

[2.5, 17.5]

Question 40

Which measure of dispersion is most affected by extreme values?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range

Question 41

The variance of a data set is always:

Accepted Answer

A non-negative value

Answer

A value less than or equal to zero

Answer

Equal to zero

Answer

Dependent on the mean of the data

Question 42

The variance of a data set with all values identical is:

Accepted Answer

0

Answer

1

Answer

Equal to the value itself

Answer

Cannot be determined