Measures of Dispersion: Understanding Data Spread in Business Statistics

Question 1

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

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Coefficient of variation

Question 2

In business statistics, the primary purpose of measures of dispersion is to:

Accepted Answer

Compare the variability of different datasets.

Answer

Identify the central tendency of a dataset.

Answer

Determine the shape of a probability distribution.

Answer

Predict future values of a variable.

Question 3

Which of the following is NOT a measure of dispersion used to describe the spread of data?

Accepted Answer

Correlation coefficient

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 4

Which measure of dispersion is most affected by extreme values in a dataset?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Question 5

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

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 6

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 7

A data set with a large range indicates:

Accepted Answer

High variability of data

Answer

Low variability of data

Answer

No variability of data

Answer

Cannot be determined from the given information

Question 8

The variance of a data set is defined as:

Accepted Answer

Sum of squared deviations from the mean divided by the number of observations

Answer

Sum of deviations from the mean divided by the number of observations

Answer

Sum of squared deviations from the mean

Answer

Cannot be determined from the given information

Question 9

Which data set would typically have the largest standard deviation?

Accepted Answer

Data set with values spread out far from the mean

Answer

Data set with values close to the mean

Answer

Data set with a small number of observations

Answer

Cannot be determined from the given information

Question 10

Calculate the variance of the data set: {1, 3, 5, 7, 9}

Accepted Answer

8

Answer

4

Answer

12

Answer

16

Question 11

Which data set exhibits the greatest variability?

Accepted Answer

{1, 3, 5, 7, 9}

Answer

{1, 1, 1, 1, 1}

Answer

{0, 1, 2, 3, 4}

Answer

{0, 2, 4, 6, 8}

Question 12

Define variance, and provide its formula to calculate it.

Accepted Answer

Variance measures the spread or dispersion of data, calculated as the average of the squared differences between each data point and the mean.

Answer

Variance is the square root of the standard deviation, a measure of data spread.

Answer

Variance is the sum of all data points divided by the mean, indicating data variability.

Answer

Variance measures the distance between the minimum and maximum data points, indicating data range.

Question 13

Which measure of dispersion indicates the average spread of data points from the central point?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 14

A dataset has a variance of 16. What is its standard deviation?

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 15

Which of the following is NOT an advantage of using variance as a measure of dispersion?

Accepted Answer

It cannot have negative values

Answer

It is based on all data points

Answer

It is simple to calculate

Answer

It accounts for the magnitude of deviations

Question 16

A company recorded monthly sales data with the following values: 12, 18, 24, 30, 36. What is the range of this data?

Accepted Answer

6

Answer

12

Answer

18

Answer

24

Question 17

A population has a mean of 40 and a standard deviation of 5. If a sample of 49 is taken from this population, what is the expected standard deviation of the sample?

Accepted Answer

2.5

Answer

1

Answer

5

Answer

10

Question 18

Which of the following factors does NOT affect the variance of a dataset?

Accepted Answer

Central tendency

Answer

Spread of data

Answer

Number of data points

Answer

Type of data distribution

Question 19

A company wants to compare the variability of sales in two different regions. Which measure of dispersion is most appropriate?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Range

Answer

Median

Question 20

Which of the following measures of dispersion is a measure of the average squared deviation from the mean?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 21

The range of a dataset is the difference between the:

Accepted Answer

Maximum and minimum values

Answer

Mean and median values

Answer

First and third quartiles

Answer

Median and mode values

Question 22

Which of the following is a unitless measure of dispersion?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 23

The coefficient of variation is calculated as:

Accepted Answer

Standard deviation / Mean

Answer

Mean / Standard deviation

Answer

Variance / Mean

Answer

Mean / Variance

Question 24

Which of the following would increase the variance of a dataset?

Accepted Answer

Multiplying each data point by a constant

Answer

Adding a constant to each data point

Answer

Removing an outlier

Answer

Adding more data points with the same value

Question 25

How can choosing different measures of dispersion affect the interpretation of data analysis results?

Accepted Answer

Different dispersion measures highlight different aspects of data variability, leading to varying interpretations.

Answer

The choice of dispersion measure has no impact on how data analysis results are interpreted.

Answer

Dispersion measures are only useful for datasets with a large sample size.

Answer

The standard deviation is always a better measure of dispersion than the range.

Question 26

How does sample size influence the reliability and generalizability of measures of dispersion?

Accepted Answer

Larger sample sizes enhance reliability and generalizability.

Answer

Smaller sample sizes lead to more reliable measures.

Answer

Sample size has no impact on dispersion measures.

Question 27

How do outliers influence the interpretation of a dataset's standard deviation and variance? Provide specific examples to demonstrate your answer.

Accepted Answer

Outliers can inflate both standard deviation and variance, making the data appear more dispersed.

Answer

Outliers enhance the reliability of standard deviation and variance as measures of data spread.

Answer

Outliers have no impact on variance but elevate the standard deviation.

Question 28

How can a large standard deviation relative to the mean help identify potential data errors or outliers?

Accepted Answer

A large standard deviation relative to the mean may indicate potential errors or outliers.

Answer

A small standard deviation relative to the mean may indicate potential errors or outliers.

Answer

The mean and standard deviation are independent measures that cannot be used to identify data errors.

Answer

The relationship between the mean and standard deviation is irrelevant to data error detection.

Question 29

Which measure of dispersion best describes the typical deviation of data points from the mean value?

Accepted Answer

Standard deviation

Answer

Variance

Answer

Range

Question 30

Which measure of dispersion is used to compare the variability of two different data sets?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 31

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

Accepted Answer

Range

Answer

Standard deviation

Answer

Variance

Answer

Interquartile range

Question 32

Which of the following is a primary advantage of using measures of dispersion?

Accepted Answer

Understanding the spread and variability of data

Answer

Determining the mean and median of a data set

Answer

Precisely predicting individual data points

Answer

Identifying outliers without considering the data distribution

Question 33

Which measure of dispersion is most influenced by extreme values in a data set?

Accepted Answer

Range

Answer

Standard deviation

Answer

Interquartile range

Answer

Variance

Question 34

Which of the following measures of dispersion is independent of the scale of measurement?

Accepted Answer

Coefficient of variation

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 35

Which of the following is a limitation of measures of dispersion?

Accepted Answer

They do not provide information about the shape of a data distribution

Answer

They can be used to compare data sets of different sizes

Answer

They can be calculated for both quantitative and qualitative data

Question 36

Which measure of dispersion calculates the difference between the largest and smallest data points?

Accepted Answer

Range

Answer

Variance

Answer

Coefficient of variation

Answer

Standard deviation

Question 37

A dataset with a variance of 120 indicates that:

Accepted Answer

The data points are spread out or dispersed widely

Answer

The standard deviation is 11

Answer

The dataset is normally distributed

Answer

The mean of the dataset is 120

Question 38

Which measure of dispersion is independent of the units of measurement?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Standard deviation

Answer

Interquartile range

Question 39

Which of the following is a disadvantage of using measures of dispersion in data analysis?

Accepted Answer

Inability to determine the exact values in a dataset

Answer

Making predictions

Answer

Understanding data variability

Answer

Comparing different datasets

Question 40

Two manufacturing plants have standard deviations of 5 and 8 units, respectively. Which plant demonstrates greater consistency in production output?

Accepted Answer

Plant A (with a standard deviation of 5 units)

Answer

Both plants have the same level of consistency

Answer

Insufficient information provided

Answer

Plant B (with a standard deviation of 8 units)

Question 41

Which measure of dispersion represents the typical distance of data points from their mean?

Accepted Answer

Standard deviation

Answer

Coefficient of variation

Answer

Variance

Answer

Range

Question 42

Which measure of dispersion is used to compare the relative variability of two or more data sets?

Accepted Answer

Coefficient of variation

Answer

Variance

Answer

Range

Answer

Standard deviation

Question 43

Which data set exhibits the greatest variability?

Accepted Answer

Data set P: {2, 6, 10, 14, 18}

Answer

Data set R: {1, 3, 5, 7, 9}

Answer

Data set V: {4, 6, 8, 10, 12}

Answer

Data set Q: {5, 5, 5, 5, 5}

Question 44

A data set has a range of 20. What does this tell us about the data?

Accepted Answer

The difference between the highest and lowest values in the data set is 20.

Answer

The average value of the data is 20.

Answer

The data is evenly distributed across the range.

Question 45

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Standard Deviation

Answer

Variance

Question 46

Two sales teams have different monthly sales variability. Team A has a standard deviation of $5,000, while Team B has a standard deviation of $2,000. What does this tell us about the teams' sales performance?

Accepted Answer

Team A has greater variability in monthly sales than Team B.

Answer

Team B has greater variability in monthly sales than Team A.

Answer

Both teams have equal variability in monthly sales.

Question 47

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

Accepted Answer

10

Answer

20

Answer

5

Answer

100

Question 48

A data set with a low standard deviation indicates what about the data points?

Accepted Answer

The data points are clustered closely around the mean.

Answer

The data points are widely spread out.

Answer

The data set has a large range.

Question 49

Two product lines have the same average sales, but product line A has a higher variance than product line B. What does this suggest about the sales performance?

Accepted Answer

Product line A has a wider range of sales values than product line B.

Answer

Product line A consistently outperforms product line B.

Answer

Product line B is more profitable than product line A.

Question 50

Two marketing campaigns are being evaluated. Campaign A has a mean click-through rate of 5% with a standard deviation of 1%, while Campaign B has a mean click-through rate of 4% with a standard deviation of 0.5%. Which campaign shows more consistency in performance?

Accepted Answer

Campaign B

Answer

Both campaigns have equal consistency.

Answer

There is not enough information to determine consistency.

Answer

Campaign A

Question 51

A data set has a range of 50 and a standard deviation of 10. Which value provides a more complete picture of the data's spread?

Accepted Answer

Standard deviation

Answer

Neither provides useful information.

Answer

Range

Answer

Both provide equal information.

Question 52

A company analyzes its customer base and finds an average age of 35 years with a standard deviation of 5 years. What can we conclude about the customer base?

Accepted Answer

Most customers are between 30 and 40 years old.

Answer

There is no meaningful conclusion that can be drawn from the data.

Answer

The customer base is evenly distributed across all age groups.

Answer

Most customers are over 40 years old.