Measures of Variability: Assess Your Understanding

Question 1

Which of the following is **not** a measure of variability in data?

Accepted Answer

Correlation

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 2

When calculating the interquartile range, what are the values that divide a dataset into four equal parts called?

Accepted Answer

Quartiles

Answer

Deciles

Answer

Percentiles

Answer

Z-scores

Question 3

The variance of a dataset is calculated by finding the average of the squared differences between each data point and the central value known as the:

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 4

A study reports a standard deviation of 10. Approximately what proportion of the data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

95%

Answer

99%

Answer

Cannot be determined

Question 5

A dataset with a mean of 50 and a standard deviation of 10 has a new value of 80 added to it. What will happen to the standard deviation?

Accepted Answer

Increase

Answer

Decrease

Answer

Remain the same

Answer

Cannot be determined

Question 6

Which of the following is NOT an advantage of using variability measures?

Accepted Answer

Making accurate predictions about future data

Answer

Summarizing the spread of data

Answer

Comparing different datasets

Answer

Providing insights into data distribution

Question 7

Which measure of variability is a squared value that quantifies the average squared deviation of data points from the mean?

Accepted Answer

Variance

Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Question 8

Which variability measure is most affected by extreme values (outliers)?

Accepted Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Answer

Variance

Question 9

A healthcare researcher wants to compare the variability of body mass index (BMI) among different age groups. Which variability measure would be most suitable for this purpose?

Accepted Answer

Coefficient of Variation

Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Question 10

Which measure of variability is most impacted by extreme values?

Accepted Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Answer

Variance

Question 11

What is a limitation of using range as a measure of variability?

Accepted Answer

It can be skewed by extreme values.

Answer

It can be negative.

Answer

It is simple to calculate.

Question 12

For data with a skewed distribution, which measure of variability is least impacted by outliers?

Accepted Answer

Interquartile Range (IQR)

Answer

Range

Answer

Standard Deviation

Question 13

The interquartile range (IQR) is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

Accepted Answer

True

Answer

False

Question 14

Standard deviation is not sensitive to outliers.

Accepted Answer

False

Answer

True

Question 15

Variance is calculated by taking the average of the squared deviations from the mean.

Accepted Answer

True

Answer

False

Question 16

Range is not sensitive to extreme values.

Accepted Answer

False

Answer

True

Question 17

Standard deviation is a measure of central tendency.

Accepted Answer

False

Answer

True

Question 18

Which measure of variability represents half the difference between the upper and lower quartiles?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 19

A dataset has a standard deviation of 10. What is the variance of the dataset?

Accepted Answer

100

Answer

10

Answer

20

Answer

0.1

Question 20

Which measure of variability is most appropriate for data that is skewed?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 21

Which of the following is a disadvantage of using range as a measure of variability?

Accepted Answer

It is affected by outliers.

Answer

It provides insight into the distribution of data.

Answer

It is straightforward to calculate.

Answer

It is always meaningful.

Question 22

Which of the following statements about variability is true?

Accepted Answer

Variability can be measured using several different statistics.

Answer

Variability is always a negative characteristic of data.

Answer

Variability is independent of the sample size.

Answer

Variability is the same as bias.

Question 23

What measure of variability represents the difference between the highest and lowest values in a dataset?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 24

Which of the following is equivalent to the square of the standard deviation?

Accepted Answer

Variance

Answer

Range

Answer

Interquartile range

Answer

Mean

Question 25

Which measure of variability allows for comparison of the spread of two different datasets?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 26

A researcher calculates the standard deviation of a dataset to be 0.25. This indicates that the data is:

Accepted Answer

Slightly variable

Answer

Highly variable

Answer

Not variable at all

Question 27

A dataset with a small standard deviation indicates:

Accepted Answer

The data values are densely clustered around the mean

Answer

The data values are widely dispersed from the mean

Answer

The data is perfectly normally distributed

Question 28

The interquartile range (IQR) is calculated as:

Accepted Answer

The difference between the upper quartile (Q3) and the lower quartile (Q1)

Answer

The difference between the maximum value and the minimum value

Answer

The sum of all data points divided by the number of data points

Answer

The square root of the variance

Question 29

The variance of a data set is defined as:

Accepted Answer

The sum of squared deviations from the mean divided by the number of data points

Answer

The difference between the largest and smallest data points

Answer

The percentile that divides the data into two equal parts

Answer

The measure of the spread of data around the mode

Question 30

Which of the following is NOT a characteristic of a normally distributed data set?

Accepted Answer

Outliers are common

Answer

Symmetrical bell shape

Answer

Median equal to mode

Answer

Mean, median, and mode are all equal

Question 31

Identify the option that does not represent a valid measure of variability in a dataset:

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Interquartile range

Question 32

The range of a dataset is mathematically determined as the difference between which values?

Accepted Answer

Highest and lowest values

Answer

Mean and median

Answer

First and third quartiles

Answer

Standard deviation and variance

Question 33

Which measure of variability is considered more resistant to the influence of outliers compared to range?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Answer

Mean

Question 34

The variance of a dataset is calculated as:

Accepted Answer

Average squared deviations from the mean

Answer

Standard deviation squared

Answer

Range divided by the number of data points

Answer

Interquartile range multiplied by the mean

Question 35

A dataset with a standard deviation of zero implies:

Accepted Answer

All data points are identical.

Answer

The data exhibits high variability.

Answer

The data follows a normal distribution.

Answer

The mean of the data is equal to zero.

Question 36

To calculate the Interquartile Range (IQR), which data values are used?

Accepted Answer

First and third quartiles

Answer

Minimum and maximum values

Answer

Median and mean

Answer

Mean and standard deviation

Question 37

Standard deviation is a measure of:

Accepted Answer

How spread out the data is around the mean

Answer

The difference between the maximum and minimum values

Answer

The number of data points in the dataset

Answer

The shape of the data distribution

Question 38

Which formula is used to calculate the variance of a dataset?

Accepted Answer

Standard deviation squared

Answer

(Maximum - Minimum) / 2

Answer

IQR / 2

Answer

Mean - Median

Question 39

A larger variance indicates that the data is:

Accepted Answer

More spread out from the mean

Answer

More concentrated around the mean

Answer

Skewed towards higher values

Answer

Normally distributed

Question 40

Which measure of variability calculates the difference between the maximum and minimum values in a dataset?

Accepted Answer

Range

Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Question 41

Which formula is used to calculate the standard deviation of a population?

Accepted Answer

σ = √(Σ(x - μ)² / N)

Answer

σ² = √(Σ(x - μ)² / N)

Answer

σ = Σ(x - μ)² / N

Answer

σ² = Σ(x - μ)² / N

Question 42

Which limitation of the range as a measure of variability is due to its sensitivity to extreme values?

Accepted Answer

It can be misleadingly large when there are outliers.

Answer

It does not take into account the distribution of the data.

Answer

It is difficult to calculate.

Answer

It cannot be used to compare different datasets.