Master Measures of Central Tendency and Dispersion in Data Analytics

Question 1

The standard deviation measures the:

Accepted Answer

Spread of data around the mean

Answer

Central point of a data set

Answer

Skewness of a data distribution

Question 2

Which measure of central tendency is best for non-numerical data?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Question 3

Which measure of dispersion is unaffected by the units of measurement?

Accepted Answer

Coefficient of variation

Answer

Variance

Answer

Standard deviation

Question 4

A coefficient of variation of 0.3 indicates that the data is:

Accepted Answer

Moderately variable

Answer

Highly variable

Answer

Not very variable

Question 5

Which of the following data sets exhibits the lowest variance?

Accepted Answer

{1, 1, 1, 1, 1}

Answer

{1, 2, 3, 4, 5}

Answer

{0, 5, 10, 15, 20}

Question 6

Which measure of central tendency is highly influenced by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 7

A data set contains the values: 5, 7, 9, 11, 13. What is the median of this data set?

Accepted Answer

9

Answer

6

Answer

10

Answer

12

Question 8

A company's sales data has a variance of 2500. What is the corresponding standard deviation?

Accepted Answer

15.81

Answer

50

Answer

100

Answer

250

Question 9

Which graphical representation is most appropriate for displaying the dispersion of a data set?

Accepted Answer

Histogram

Answer

Scatter plot

Answer

Bar chart

Answer

Line chart

Question 10

Which of the following is not considered a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 11

Which of the following is the best definition of the median?

Accepted Answer

The middle value of a data set when arranged in numerical order

Answer

The average of all values in a data set

Answer

The value that occurs most frequently in a data set

Answer

The sum of all values in a data set divided by the number of values

Question 12

Which measure of dispersion quantifies the spread of data values around their mean?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 13

What does a standard deviation of one imply about data distribution?

Accepted Answer

The data is clustered around the mean

Answer

The data is widely dispersed

Answer

The data is skewed

Answer

The data is normally distributed

Question 14

Which measure of central tendency is most heavily influenced by outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 15

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

Accepted Answer

Standard Deviation

Answer

Range

Answer

Variance

Question 16

Which of the following data sets exhibits the greatest variability?

Accepted Answer

{6, 9, 12, 15}

Answer

{10, 10, 10, 10}

Answer

{8, 10, 12, 14}

Question 17

What is the mode of the following data set: {1, 2, 3, 3, 4, 5, 5, 5, 5}

Accepted Answer

5

Answer

1

Answer

3

Answer

No mode

Question 18

Which measure of central tendency is most appropriate when dealing with a distribution that is not normally distributed?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 19

Which of the following is a limitation of using the range as a measure of dispersion?

Accepted Answer

It only provides the extreme values

Answer

It is not sensitive to outliers

Answer

It is difficult to interpret

Answer

It affects the mean

Question 20

Which measure of central tendency is not affected by extreme values?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 21

A dataset has a range of 20. If the minimum value is 10, what is the maximum value?

Accepted Answer

30

Answer

10

Question 22

Which of the following is NOT a measure of variability?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Question 23

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

Accepted Answer

100

Answer

10

Question 24

Which of the following is a limitation of using the mode as a measure of central tendency?

Accepted Answer

Can be misleading for multimodal distributions

Answer

Can be influenced by outliers

Answer

Can be difficult to calculate

Question 25

Which measure of dispersion provides the most accurate representation of data spread?

Accepted Answer

Standard deviation

Answer

Range

Question 26

The sum of squared deviations from which measure of central tendency is minimized?

Accepted Answer

Mean

Answer

Median

Question 27

In a dataset with a high variance, we can conclude that:

Accepted Answer

The data is widely dispersed

Answer

The data is clustered closely around the mean

Question 28

When analyzing a skewed data set, which measure of central tendency is most appropriate to use?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 29

Which of the following is not a measure of central tendency?

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 30

The median of a dataset represents the:

Accepted Answer

Middle value when the data is arranged in ascending order

Answer

Value that occurs most frequently

Answer

Sum of all values divided by the number of values

Answer

Average distance of each data point from the mean

Question 31

The range of a dataset is calculated as:

Accepted Answer

Difference between the maximum and minimum values

Answer

Sum of all values divided by the number of values

Answer

Average distance of each data point from the median

Answer

Standard deviation multiplied by 2

Question 32

Which measure of dispersion is a squared value?

Accepted Answer

Variance

Answer

Standard deviation

Answer

Range

Answer

Coefficient of variation

Question 33

Which of the following is a dimensionless measure of dispersion?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 34

The measures of central tendency and dispersion can be used to:

Accepted Answer

Describe and analyze data distributions

Answer

Predict future data values

Answer

Determine the probability of events

Answer

Test hypotheses about population parameters

Question 35

Which of the following is a common interpretation of a standard deviation of 10?

Accepted Answer

About 68% of the data is within 10 units of the mean

Answer

The data is spread out over a range of 10 units

Answer

The mean of the data is 10

Answer

The median of the data is 10

Question 36

When comparing two datasets with different means and standard deviations, which measure of dispersion is more appropriate?

Accepted Answer

Coefficient of variation

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 37

Under which condition is the range an appropriate measure of dispersion?

Accepted Answer

When the data is symmetric and has no significant outliers.

Answer

When the data is skewed.

Answer

When the data has a large number of data points.

Question 38

Which factor is most likely to cause an outlier in a data set?

Accepted Answer

Data entry error

Answer

Duplicate measurements

Answer

Normal distribution

Answer

Random sampling

Question 39

How do measures of dispersion help us build confidence intervals for a sample mean?

Accepted Answer

By estimating the standard error of the mean

Answer

By identifying outliers in the sample

Answer

By determining the shape of the distribution

Answer

By comparing two different samples

Question 40

For ordinal data, which measure of central tendency is most suitable?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 41

Which measure of central tendency represents the value with the highest frequency of occurrence within a dataset?

Accepted Answer

Mode

Answer

Range

Answer

Median

Answer

Mean

Question 42

Given a dataset with a standard deviation of 10, what is the approximate probability of randomly selecting a data point that lies within one standard deviation of the mean?

Accepted Answer

68%

Answer

80%

Answer

50%

Answer

95%

Question 43

Which characteristic of a measure of dispersion is undesirable?

Accepted Answer

Susceptibility to being influenced by outliers

Answer

Incorporating all data points

Answer

Responsiveness to changes in data

Answer

Ease of interpretation

Question 44

For skewed data, which measure of central tendency is most appropriate to use?

Accepted Answer

Median

Answer

Mode

Answer

Range

Answer

Mean

Question 45

In a dataset with a mean of 50 and a standard deviation of 10, what is the approximate probability of randomly selecting a data point that falls between 40 and 60?

Accepted Answer

68%

Answer

80%

Answer

95%

Answer

50%

Question 46

Given a dataset with a mean of 70, a standard deviation of 12, a lower quartile of 60, and an upper quartile of 80, what is the interquartile range (IQR) of the dataset?

Accepted Answer

20

Answer

25

Answer

15

Answer

30

Question 47

Which measure of central tendency indicates the value that occurs most frequently in a dataset?

Accepted Answer

Mode

Answer

Median

Answer

Range

Answer

Mean

Question 48

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Variance

Answer

Interquartile range

Answer

Standard deviation

Question 49

A dataset has a positively skewed distribution. Which measure of central tendency would be most appropriate to use?

Accepted Answer

Median

Answer

Mean

Answer

Standard deviation

Answer

Mode

Question 50

A marketing manager wants to understand the typical age of customers buying a specific product. Which measure of central tendency would best represent this 'typical' age?

Accepted Answer

Mean

Answer

Mode

Answer

Median

Answer

Range

Question 51

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Mode

Answer

Median

Question 52

A company's employee salary data is heavily skewed to the right due to a few very high earners. Which measure of central tendency best represents the 'typical' salary in this scenario?

Accepted Answer

Median

Answer

Mode

Answer

Range

Answer

Mean

Question 53

The ages of students in a class are: 20, 21, 21, 22, 22, 22, 23. What is the mode of this data set?

Accepted Answer

22

Answer

22.5

Answer

21

Answer

21.5

Question 54

Which measure of dispersion calculates the average distance of each data point from the mean?

Accepted Answer

Standard Deviation

Answer

Variance

Answer

Range

Answer

Interquartile Range

Question 55

A stock analyst wants to measure the price volatility of a specific stock over the past year. Which measure of dispersion is most suitable for this purpose?

Accepted Answer

Standard Deviation

Answer

Median

Answer

Mode

Answer

Mean

Question 56

The interquartile range (IQR) is a measure of dispersion that focuses on which part of the data distribution?

Accepted Answer

The middle 50%

Answer

The bottom 25%

Answer

The top 25%

Answer

The entire range

Question 57

If a data set has a variance of 25, what is the standard deviation?

Accepted Answer

5

Answer

12.5

Answer

50

Answer

625

Question 58

A small standard deviation indicates that the data points are:

Accepted Answer

Closely clustered around the mean

Answer

Widely spread around the mean

Answer

Skewed to the right

Answer

Skewed to the left

Question 59

Which statement is true about the relationship between the range and the interquartile range?

Accepted Answer

The range is always greater than or equal to the interquartile range.

Answer

The range is always equal to the interquartile range.

Answer

The range is always less than or equal to the interquartile range.