Measures of Central Tendency: Mean, Median, Mode, and Applications

Question 1

Which measure of central tendency is highly susceptible to extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 2

Calculate the average of the following data set: {2, 4, 6, 8, 10}

Accepted Answer

5

Answer

4

Answer

6

Answer

8

Question 3

Identify the data set that has 5 as its most frequently occurring value:

Accepted Answer

{3, 5, 5}

Answer

{2, 5, 7}

Answer

{5, 5, 6}

Answer

{4, 5, 6, 8}

Question 4

In a skewed distribution, which statement about the mean and median is correct?

Accepted Answer

Mean can be greater than or less than the median depending on the skewness.

Answer

Mean is always greater than the median.

Answer

Mean is always less than the median.

Answer

Mean and median can be equal.

Question 5

Which measure of central tendency is most heavily influenced by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 6

Given the data set {5, 7, 10, 12, 15}, what is the mode of the data set?

Accepted Answer

10

Answer

5

Answer

7

Question 7

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

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 8

A data set has a z-score of 1.5, a mean of 12, and a standard deviation of 2. What is the corresponding value of the data point?

Accepted Answer

14

Answer

10

Answer

12

Question 9

Which drawback is associated with using the mean as a measure of central tendency?

Accepted Answer

Susceptibility to distortion by outliers

Answer

Inability to represent the typical value

Answer

Restriction to quantitative data

Question 10

Which measure of central tendency is most susceptible to extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 11

Which measure of central tendency is defined as the sum of all values divided by the number of values in a dataset?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 12

Which measure of central tendency is most suitable when the data distribution is skewed?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 13

Which measure of central tendency can have multiple values?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Question 14

A dataset consists of the following values: 10, 12, 14, 16, 16, 18, 20. Calculate the median.

Accepted Answer

16

Answer

14

Answer

18

Answer

20

Question 15

Consider a distribution with a mean of 10 and a median of 12. Which of the following statements accurately describes the distribution?

Accepted Answer

The distribution is skewed to the right.

Answer

The distribution is skewed to the left.

Answer

The distribution is symmetric.

Answer

The distribution is bimodal.

Question 16

What is the definition of weighted mean?

Accepted Answer

The sum of data points multiplied by their respective weights, divided by the total number of data points.

Answer

The middle value of the data when arranged in ascending order.

Answer

The value that occurs most frequently in a data set.

Answer

The average of the mean and median.

Question 17

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

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 18

Which measure of central tendency is heavily influenced by extreme values, making it less representative of the majority of data points?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 19

For a data set with values {3, 5, 5, 7, 9}, which of the following is the median?

Accepted Answer

5

Answer

3

Answer

6

Answer

7

Question 20

Which measure of central tendency represents the value that occurs most frequently in a data set?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Question 21

In the case of a skewed distribution, which measure of central tendency is more representative of the majority of the data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 22

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

Accepted Answer

It can be easily influenced by outliers.

Answer

It can only be used for numerical data.

Answer

It requires complex calculations.

Question 23

In a data set with values {2, 2, 3, 3, 4, 4, 5, 5}, what is/are the mode(s)?

Accepted Answer

2 and 4

Answer

2

Answer

4

Answer

2, 3, 4, and 5

Question 24

For skewed data distributions, which measure of central tendency provides a better representation of the typical value?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 25

Given the data set: {5, 7, 9, 12, 15, 17, 19}, calculate the median, which represents the middle value when the data is arranged in ascending order.

Accepted Answer

12

Answer

9

Answer

15

Question 26

Which measure of central tendency is suitable for ordinal data, where values represent categories or ranks?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 27

Which measure of central tendency is calculated by summing all values in a data set and dividing by the total number of values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 28

When conducting hypothesis testing, which measure of central tendency is most suitable for distributions that may have outliers or extreme values?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 29

Which measure of central tendency is calculated by summing all values in a dataset and dividing by the total number of values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 30

What is the measure of central tendency that identifies the middle value of a dataset when assorted in ascending or descending order?

Accepted Answer

Median

Answer

Mean

Answer

Variance

Answer

Mode

Question 31

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

Accepted Answer

Mode

Answer

Standard deviation

Answer

Median

Answer

Mean

Question 32

Which measure of central tendency is most susceptible to extreme values or outliers?

Accepted Answer

Mean

Answer

Mode

Answer

Median

Answer

Standard deviation

Question 33

Which measure of central tendency is used to determine the expected value of a random variable?

Accepted Answer

Mean

Answer

Mode

Answer

Variance

Answer

Median

Question 34

What is the key difference between the mean and the median?

Accepted Answer

Mean is affected by outliers, while median is not.

Answer

Median is always greater than the mean.

Answer

Mean and median are always equal.

Answer

Mean is always greater than the median.

Question 35

Which measure of central tendency is most appropriate for analyzing data that contains extreme values or outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 36

Which measure of central tendency is most significantly influenced by extreme values, such as outliers?

Accepted Answer

Mean

Answer

Mode

Answer

Range

Answer

Median

Question 37

Given the dataset: {10, 12, 14, 16, 18}, determine the median value.

Accepted Answer

14

Answer

12

Answer

15

Answer

17

Question 38

Which measure of central tendency is calculated by summing all values in a dataset and dividing by the count of values?

Accepted Answer

Mean

Answer

Median

Answer

Standard deviation

Answer

Mode

Question 39

Which measure of central tendency is defined as the value that divides a dataset into two equal halves when ranked in order?

Accepted Answer

Median

Answer

Frequency

Answer

Mode

Answer

Mean

Question 40

In the context of a distribution that is skewed, which measure of central tendency is most suitable for representing the central value?

Accepted Answer

Median

Answer

Range

Answer

Mean

Answer

Mode

Question 41

In a survey of 100 people about their monthly income, the most frequently reported income is $3,000. What is the mode of the surveyed income data?

Accepted Answer

$3,000

Answer

$2,000

Answer

$5,000

Answer

$4,000

Question 42

Which measure of central tendency measures the average distance of data points from their mean value?

Accepted Answer

Standard deviation

Answer

Median

Answer

Variance

Answer

Mean

Question 43

Which measure of central tendency is most heavily impacted by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 44

A mid-sized firm's weekly sales data for the past month are as follows: [$10,000, $12,000, $11,000, $14,000, $15,000, $12,500, $13,000]. Determine the median sales amount.

Accepted Answer

$12,500

Answer

$12,000

Answer

$14,000

Answer

$10,000

Question 45

Which of the following is not a characteristic of the mean?

Accepted Answer

It is unaffected by outliers.

Answer

It is the sum of all values divided by the number of values.

Answer

It can be used to compare data sets of different sizes.

Answer

It can be a non-integer value.

Question 46

The weights (in pounds) of a sample of 10 adult males are: [150, 160, 170, 180, 190, 200, 210, 220, 230, 240]. Calculate the range of these weights.

Accepted Answer

90 pounds

Answer

240 pounds

Answer

150 pounds

Answer

100 pounds

Question 47

Which of the following data sets exhibits the greatest variance?

Accepted Answer

[10, 20, 30, 40, 50]

Answer

[10, 15, 20, 25, 30]

Answer

[5, 10, 15, 20, 25]

Answer

[0, 5, 10, 15, 20]

Question 48

Which measure of central tendency is most suitable for ordinal data?

Accepted Answer

Median

Answer

Range

Answer

Mode

Answer

Mean

Question 49

Identify the mode of the following data set: 2, 5, 3, 5, 2, 5, 7, 2, 5

Accepted Answer

5

Answer

3

Answer

2

Question 50

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

Accepted Answer

Mean

Answer

Median

Answer

All are equally influenced

Answer

Mode

Question 51

In a perfectly symmetrical distribution, how are the mean, median, and mode related?

Accepted Answer

They have the same value.

Answer

The median is lower than the mode.

Answer

The mean is higher than the median.

Answer

The mode is lower than the median.

Question 52

A shoe store wants to stock the most popular shoe size. Which measure of central tendency should they use to determine the demand?

Accepted Answer

Mode

Answer

Median

Answer

Mean

Question 53

On a test, the mean score was 75 with a standard deviation of 5. What does the standard deviation indicate?

Accepted Answer

The typical spread or variability of scores around the mean.

Answer

The highest score achieved on the test.

Answer

The lowest score on the test.

Question 54

You are examining income distribution in a region with known high income inequality. Which measure of central tendency would provide the most representative view of the 'typical' income?

Accepted Answer

Median

Answer

Range

Answer

Mode

Answer

Mean