Measures of Central Tendency: The Heart of Data Distribution

Question 1

A data set comprises the values: 4, 6, 8, 10, 12. Calculate its mean.

Accepted Answer

8

Answer

6

Answer

10

Answer

12

Question 2

Which characteristic does NOT apply to the median?

Accepted Answer

Always an integer

Answer

Resistant to outliers

Answer

Divides the data set in half

Answer

Represents the middle value

Question 3

A histogram exhibits a symmetrical and bell-shaped distribution. Which type of distribution does it most likely represent?

Accepted Answer

Normal distribution

Answer

Skewed distribution

Answer

Bimodal distribution

Answer

Trimodal distribution

Question 4

Given a data set with a mean of 20 and a standard deviation of 4, determine the approximate percentage of values that are within one standard deviation from the mean.

Accepted Answer

68%

Answer

38%

Answer

80%

Answer

95%

Question 5

Calculate the mean of the following dataset: 10, 12, 15, 15, 18

Accepted Answer

14

Answer

12

Answer

16

Question 6

Which option is NOT considered a measure of variability?

Accepted Answer

Median

Answer

Range

Answer

Standard deviation

Question 7

In a negatively skewed distribution, which statement is true?

Accepted Answer

Median is greater than the mean

Answer

Mean is greater than the median

Answer

Mode is greater than the median

Question 8

A distribution exhibits a phenomenon where it possesses three modes. What is this characteristic termed?

Accepted Answer

Multimodality

Answer

Bimodality

Answer

Skewness

Question 9

In a data set with the values 2, 4, 5, 7, and 9, what is the median value?

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 10

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

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Variance

Question 11

A data set with a large standard deviation indicates that:

Accepted Answer

The data is spread out widely

Answer

The data is clustered around the mean

Answer

The mean is high

Answer

The median is low

Question 12

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

Bimodal

Answer

Bell-shaped

Answer

Symmetrical

Answer

Mean = Median = Mode

Question 13

Two data sets have the same mean and median but different standard deviations. Which data set has a greater variability?

Accepted Answer

The data set with the larger standard deviation

Answer

The data set with the smaller standard deviation

Answer

Both data sets have equal variability

Answer

There is not enough information to determine

Question 14

What is a key advantage of using the median as a measure of central tendency?

Accepted Answer

It is not influenced by extreme values.

Answer

It is particularly easy to calculate.

Answer

It offers a more accurate representation of the data's center than the mean.

Answer

It can be applied to both numerical and categorical data.

Question 15

What is the fundamental difference between the mode and the mean?

Accepted Answer

The mode represents the value that occurs most frequently, while the mean represents the average of all values.

Answer

The mode represents the average of all values, while the mean represents the value that occurs most frequently.

Answer

The mode is applicable to categorical data, while the mean is applicable to numerical data.

Answer

The mode and the mean are always identical.

Question 16

If a dataset has a range of 10, what is the difference between its maximum and minimum values?

Accepted Answer

10

Answer

5

Answer

20

Answer

1

Question 17

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

Accepted Answer

It can be negative.

Answer

It is always non-negative.

Answer

It is measured in the same units as the original data.

Answer

It is a measure of variability.

Question 18

Which measure of central tendency is the sum of all values divided by the number of values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 19

A group of scores has a mode of 10 and a median of 12. Which measure of central tendency would you recommend using to best represent the typical score?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 20

Which measure of central tendency is most appropriate for use with categorical data?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 21

Which of the following is the formula for calculating the variance?

Accepted Answer

Sum of squared deviations / (n - 1)

Answer

Sum of deviations / n

Answer

Range divided by standard deviation

Answer

Mean minus mode

Question 22

Which measure of central tendency is most resistant to outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 23

A data set has the following values: 5, 7, 9, 11, 13. What is the median?

Accepted Answer

9

Answer

6

Answer

8

Answer

10

Question 24

Which of these is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 25

When calculating the mean, the sum of all deviations from the mean is always equal to:

Accepted Answer

Zero

Answer

The standard deviation

Answer

The mode

Answer

The median

Question 26

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

Accepted Answer

Median

Answer

Mode

Answer

Mean

Answer

Standard deviation

Question 27

The range of a dataset is calculated by finding the difference between:

Accepted Answer

The maximum and minimum values

Answer

The mode and the range

Answer

The standard deviation and the variance

Answer

The mean and the median

Question 28

Which measure of central tendency does not utilize all the data values in its calculation?

Accepted Answer

Mode

Answer

Mean

Answer

Range

Answer

Median

Question 29

The standard deviation primarily measures the:

Accepted Answer

Dispersion or spread of the data

Answer

Center of the data

Answer

Skewness of the data

Answer

Frequency of the data

Question 30

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 31

Which measure of central tendency is appropriate for data measured on an ordinal scale?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 32

Identify a potential drawback of using the mean as a measure of central tendency.

Accepted Answer

Susceptibility to extreme values

Answer

Limited applicability to different data types

Answer

Inability to facilitate comparisons between datasets

Answer

Always resulting in a whole number

Question 33

A researcher is studying the number of hours students spend studying per week. They find that the most frequent study time is 10 hours. Which measure of central tendency represents this most frequent value?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 34

A researcher is examining the distribution of scores on a happiness scale. The data is skewed to the right. Which measure of central tendency is the most resistant to the influence of extreme values and thus, the most appropriate for describing the center of this skewed distribution?

Accepted Answer

Median

Answer

Mean

Answer

Range

Answer

Mode

Question 35

A psychology professor gives an exam. The scores are as follows: 85, 90, 75, 95, 80, 85. What is the mean score on the exam?

Accepted Answer

85

Answer

90

Answer

87.5

Answer

80

Question 36

A researcher is studying the salaries of employees at a company. The average salary is $60,000. However, the CEO's salary is significantly higher than the rest of the employees, skewing the average.  Which measure of central tendency would provide a more accurate representation of the typical salary in this situation, where a few extreme values influence the mean?

Accepted Answer

Median

Answer

Mode

Answer

Mean

Answer

Range

Question 37

A researcher is studying the age of participants in a study. The youngest participant is 18 years old, and the oldest is 35 years old. What is the range of the ages?

Accepted Answer

17

Answer

18

Answer

53

Answer

35

Question 38

You are analyzing data on the number of hours people spend exercising per week. You find that the mean is 3 hours, the median is 2.5 hours, and the mode is 2 hours.  What does this difference between the mean, median, and mode suggest about the distribution of the data?

Accepted Answer

The data is likely skewed to the right.

Answer

There is no clear pattern in the data.

Answer

The data is skewed to the left.

Answer

The data is normally distributed.

Question 39

Which measure of central tendency is most susceptible to being heavily influenced by extreme values (outliers) in a dataset?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 40

A researcher is studying the number of times people check their phones per day. They find that the mean is 50 times, the median is 40 times, and the mode is 30 times.  Which measure of central tendency provides the most representative value for the typical number of phone checks in this dataset, considering the potential influence of outliers?

Accepted Answer

Median

Answer

Mode

Answer

Mean

Answer

Range

Question 41

A researcher is studying the number of hours people sleep per night. They find that the data is normally distributed. Which measure of central tendency is generally the most appropriate and representative measure for the center of a normally distributed dataset?

Accepted Answer

Mean

Answer

Mode

Answer

Median

Answer

Range

Question 42

Which of the following is NOT a measure of central tendency, but rather a measure of variability or dispersion?

Accepted Answer

Standard Deviation

Answer

Median

Answer

Mean

Answer

Mode