Measures of Central Tendency: Master the Core Concepts

Question 1

The mean of a data set is calculated by summing all values and dividing by the number of values in the data set. True or False?

Accepted Answer

True

Answer

False

Question 2

The range of a data set is calculated by subtracting the minimum value from the maximum value. True or False?

Accepted Answer

True

Answer

False

Question 3

Which measure of central tendency is least affected by outliers in a data set?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 4

The standard deviation of a data set provides information about how spread out the data is. True or False?

Accepted Answer

True

Answer

False

Question 5

Which of the following is NOT a common application of measures of central tendency?

Accepted Answer

Finding the median of a data set

Answer

Summarizing data

Answer

Comparing data sets

Answer

Making predictions

Question 6

What is the definition of mean?

Accepted Answer

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

Answer

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

Answer

The most frequently occurring value in a data set

Answer

The difference between the maximum and minimum values in a data set

Question 7

Define the range of a data set.

Accepted Answer

The difference between the maximum and minimum values

Answer

The sum of all data values

Answer

The most frequently occurring value

Answer

The middle value when arranged in ascending order

Question 8

What does a higher standard deviation indicate?

Accepted Answer

More variability in the data

Answer

Less variability in the data

Answer

Equal variability in the data

Answer

No variability in the data

Question 9

Which of these is not a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 10

Which measure of central tendency is most susceptible to being affected by outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 11

Which of the following data sets has the least variance?

Accepted Answer

[1, 2, 3, 4, 5]

Answer

[2, 4, 6, 8, 10]

Answer

[1, 3, 5, 7, 9]

Answer

[0, 2, 4, 6, 8]

Question 12

Which measure of central tendency is most appropriate for data that is ranked or ordered?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 13

Identify the median of the following data set: 5, 7, 3, 9, 1

Accepted Answer

5

Answer

3

Answer

7

Answer

9

Question 14

Which characteristic does NOT apply to the mode?

Accepted Answer

It can be used to compare different data sets.

Answer

It represents the value that occurs most frequently in a data set.

Answer

It can be calculated for both discrete and continuous data.

Answer

It can be influenced by extreme values.

Question 15

The standard deviation of a data set measures:

Accepted Answer

The dispersion of data points around the mean.

Answer

The average distance of data points from the mean.

Answer

The value that occurs most frequently in the data set.

Answer

The difference between the maximum and minimum values.

Question 16

Which data set exhibits the largest variance?

Accepted Answer

3, 7, 11, 15, 19

Answer

5, 5, 5, 5, 5

Answer

4, 6, 8, 10, 12

Answer

2, 4, 6, 8, 10

Question 17

In a normal distribution, approximately what percentage of data points fall within one standard deviation of the mean?

Accepted Answer

68.2%

Answer

34.1%

Answer

50%

Answer

95.4%

Question 18

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

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 19

The standard deviation of a data set measures its:

Accepted Answer

Variability

Answer

Central tendency

Answer

Shape

Answer

Distribution

Question 20

Which of the following measures is most appropriate for skewed data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 21

The mode of a data set is the value that:

Accepted Answer

Occurs most frequently

Answer

Is the middle value

Answer

Is the sum of all values divided by the number of values

Answer

Is the difference between the highest and lowest values

Question 22

Which of the following is NOT a measure of dispersion (spread) in a dataset?

Accepted Answer

Median

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 23

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 24

The standard deviation of a data set measures its:

Accepted Answer

Spread

Answer

Average

Answer

Center

Answer

Range

Question 25

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

Accepted Answer

Percentile

Answer

Mean

Answer

Median

Answer

Mode

Question 26

Calculate the mean of the data set {1, 3, 5, 7, 9}.

Accepted Answer

6

Answer

2

Answer

4

Answer

8

Question 27

Identify the mode of the data set {2, 4, 4, 6, 8}.

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 28

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

Accepted Answer

Correlation coefficient

Answer

Mean

Answer

Median

Answer

Mode

Question 29

Which of the following data sets has the largest range?

Accepted Answer

4, 8, 12, 16, 20

Answer

1, 3, 5, 7, 9

Answer

2, 4, 6, 8, 10

Answer

3, 6, 9, 12, 15

Question 30

What is the primary purpose of using a box plot?

Accepted Answer

To illustrate the distribution of data.

Answer

To compare data sets.

Answer

To detect outliers.

Answer

To calculate measures of central tendency.

Question 31

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

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 32

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

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 33

The data set {5, 7, 9, 11, 13} is given. What is the median of this data set?

Accepted Answer

9

Answer

7

Answer

11

Answer

13

Question 34

Which measure of central tendency describes the spread or dispersion of data?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 35

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

Accepted Answer

Correlation

Answer

Mean

Answer

Median

Answer

Mode

Question 36

Which of the following formulas is used to calculate the variance of a data set?

Accepted Answer

Variance = Sum of squared deviations from the mean / (Number of data points - 1)

Answer

Variance = Sum of deviations from the mean / Number of data points

Answer

Variance = Standard deviation squared

Answer

Variance = Mean squared

Question 37

Six students took a test, scoring the following marks: 75, 80, 82, 85, 90, and 92. What is the average (mean) score for the test?

Accepted Answer

84

Answer

90

Answer

82

Answer

85

Question 38

Five puppies are weighed, with the following weights: 2.5kg, 2.8kg, 3.1kg, 2.7kg, and 3.0kg. What is the median weight of the puppies?

Accepted Answer

2.8kg

Answer

2.5kg

Answer

2.7kg

Answer

3.0kg

Question 39

A survey asks people about their favorite color. The results are: Blue (12), Red (8), Green (5), Blue (10), Yellow (6), Blue (9). What is the mode (most frequent color)?

Accepted Answer

Blue

Answer

Red

Answer

Yellow

Answer

Green

Question 40

A set of data has an average (mean) of 15 and a standard deviation of 3. Which value is within one standard deviation of the mean?

Accepted Answer

17

Answer

20

Answer

10

Answer

25

Question 41

If the variance of a dataset is 16, what is the standard deviation?

Accepted Answer

4

Answer

8

Answer

16

Answer

64

Question 42

Which measure of central tendency is most influenced by extreme values (outliers)?

Accepted Answer

Mean

Answer

Mode

Answer

Range

Answer

Median

Question 43

A teacher wants to know the most popular book genre among students. Which measure of central tendency would be most helpful?

Accepted Answer

Mode

Answer

Median

Answer

Range

Answer

Mean

Question 44

The heights of 100 students are normally distributed with a mean of 160cm and a standard deviation of 5cm. About how many students are between 155cm and 165cm tall?

Accepted Answer

68

Answer

50

Answer

95

Answer

34

Question 45

Two sets of data have the same average (mean) but different standard deviations. What does this tell us about the datasets?

Accepted Answer

The datasets have different spreads or variability.

Answer

The datasets have different means.

Answer

The datasets are identical.

Question 46

A set of data has the following values: 5, 8, 10, 12, 15. What is the mean of this data set?

Accepted Answer

10

Answer

8

Answer

15

Answer

12

Question 47

The ages of students in a class are: 15, 16, 16, 17, 17, 17, 18. What is the median age?

Accepted Answer

17

Answer

16

Answer

18

Answer

15

Question 48

A shop sells the following sizes of shoes: 6, 7, 7, 8, 8, 8, 9, 9. What is the mode of these shoe sizes?

Accepted Answer

8

Answer

7

Answer

6

Answer

9

Question 49

The heights of five students are 160 cm, 165 cm, 170 cm, 175 cm, and 180 cm. What is the range of their heights?

Accepted Answer

20 cm

Answer

10 cm

Answer

25 cm

Answer

15 cm

Question 50

A data set has a mean of 10 and a standard deviation of 2. Which of the following values would be considered an outlier?

Accepted Answer

16

Answer

12

Answer

6

Answer

8

Question 51

Two data sets have the same mean but different standard deviations. Which statement is true about the data sets?

Accepted Answer

The data set with the larger standard deviation has more spread.

Answer

Both data sets have the same spread.

Answer

The data set with the larger standard deviation has less spread.

Question 52

The variance of a data set is 9. What is the standard deviation?

Accepted Answer

3

Answer

1

Answer

9

Answer

81

Question 53

A company wants to compare the average salaries of its employees in two different departments. Which measure of central tendency would be most appropriate?

Accepted Answer

Mean

Answer

Mode

Answer

Range

Answer

Median

Question 54

A teacher wants to understand the typical performance of students on a test. Which measure of central tendency would be most helpful?

Accepted Answer

Mean

Answer

Median

Answer

Range

Answer

Mode

Question 55

A survey asks people to rate their satisfaction with a product on a scale of 1 to 5. Which measure of central tendency would be most appropriate to analyze the results?

Accepted Answer

Median

Answer

Range

Answer

Mode

Answer

Mean