Measures of Spread: Understanding Data Variability

Question 1

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

Accepted Answer

Sum of squared deviations from the mean / (n - 1)

Answer

Sum of deviations from the mean / (n + 1)

Answer

Sum of squared deviations from the mean / n

Answer

Mean of squared deviations from the mean

Question 2

Which measure of spread is most suitable for the dataset: 1, 3, 5, 7, 9?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Question 3

The range of a dataset is the difference between its maximum and minimum values. A dataset has a range of 12. What is the difference between the largest and smallest values in the dataset?

Accepted Answer

12

Answer

6

Answer

18

Answer

24

Question 4

A dataset has a mean of 50 and a range of 20. What is the smallest possible value in the dataset?

Accepted Answer

30

Answer

40

Answer

50

Answer

60

Question 5

Which of these is NOT a measure of spread?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 6

The range of a dataset is calculated as the difference between its:

Accepted Answer

Maximum and minimum values

Answer

Mean and median values

Answer

First and third quartiles

Answer

Mean and standard deviation

Question 7

The variance of a dataset is defined as the:

Accepted Answer

Average of the squared deviations from the mean

Answer

Average of the absolute deviations from the mean

Answer

Sum of the differences between the data points

Answer

Square of the standard deviation

Question 8

A dataset has a mean of 10 and a standard deviation of 2. What is the z-score of a value of 14?

Accepted Answer

1

Answer

0.5

Answer

2

Answer

4

Question 9

Which measure of spread represents the average distance of data points from their mean?

Accepted Answer

Standard deviation

Answer

Range

Answer

Variance

Question 10

The interquartile range (IQR) of a dataset is:

Accepted Answer

Difference between first and third quartiles

Answer

Difference between median and mean

Answer

Average of range and variance

Answer

Reciprocal of standard deviation

Question 11

Which measure of spread is most affected by outliers?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range

Question 12

Which measure of spread represents the difference between the maximum and minimum values in a dataset?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Covariance

Question 13

Standard deviation is defined as the square root of variance. What is the standard deviation of the dataset {10, 12, 14, 16, 18}?

Accepted Answer

2.83

Answer

2

Answer

3

Answer

4

Question 14

The range of a set of data is the difference between the ____ and the ____.

Accepted Answer

Maximum, minimum

Answer

Mean, median

Answer

Median, mode

Answer

Mode, minimum

Question 15

The standard deviation of a set of data is equal to:

Accepted Answer

The square root of the variance

Answer

The square of the variance

Answer

The reciprocal of the variance

Answer

Twice the variance

Question 16

A data set has a range of 10 and a standard deviation of 2. What is the variance of the data set?

Accepted Answer

4

Answer

2

Answer

10

Answer

20

Question 17

Which of the following data sets has the greatest spread?

Accepted Answer

{1, 2, 20, 40, 60}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 2, 3, 20, 21}

Answer

{1, 2, 3, 4, 20}

Question 18

Which measure of spread quantifies the typical distance of data points from their mean?

Accepted Answer

Standard deviation

Answer

Range

Answer

Variance

Question 19

Which characteristic describes variance?

Accepted Answer

It measures the dispersion of data points around their mean.

Answer

It can take on negative values.

Answer

It is expressed as a whole number.

Question 20

Which of the following is NOT a purpose of using measures of spread?

Accepted Answer

Forecasting future data values

Answer

Comparing multiple data sets

Answer

Identifying unusual data points

Question 21

Which unit of measurement is suitable for expressing the standard deviation of weights?

Accepted Answer

Kilograms

Answer

Centimetres

Answer

Litres

Answer

Years

Question 22

A test score of 80 was obtained in a class with a mean of 75 and a standard deviation of 5. What is its z-score?

Accepted Answer

0.25

Answer

1

Answer

-1

Answer

2

Question 23

The standard deviation of a dataset measures:

Accepted Answer

Spread

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 24

Which measure of spread is most sensitive to outliers?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range

Question 25

Which measure of spread is most influenced by extreme values?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Question 26

The range of a dataset is 10. What is the greatest possible difference between the maximum and minimum values?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 27

Which of the following datasets has the largest spread?

Accepted Answer

[2, 4, 6, 8, 10]

Answer

[1, 2, 3, 4, 5]

Answer

[1, 3, 5, 7, 9]

Answer

[0, 2, 4, 6, 8]

Question 28

The scatterplot of two variables shows a strong positive correlation. What can we infer about the standard deviation of the residuals?

Accepted Answer

It is likely to be small.

Answer

It is likely to be large.

Answer

It is likely to be zero.

Answer

This cannot be determined from the given information.

Question 29

Which of the following is NOT a measure of spread?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 30

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

Accepted Answer

Smallest and largest values

Answer

Mean and median

Answer

First and third quartiles

Answer

Lower and upper quartiles

Question 31

Which dataset has the largest standard deviation?

Accepted Answer

[0, 5, 10, 15, 20]

Answer

[1, 2, 3, 4, 5]

Answer

[0, 2, 4, 6, 8]

Answer

[1, 3, 5, 7, 9]

Question 32

The interquartile range (IQR) of a dataset is the difference between the:

Accepted Answer

Upper and lower quartiles

Answer

Mean and median

Answer

Range of the middle 50% of the data

Answer

Standard deviation of the data

Question 33

A measure of the central tendency of a dataset is:

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

IQR

Question 34

A dataset with a high standard deviation is:

Accepted Answer

Widely spread

Answer

Narrowly spread

Answer

Symmetrical

Answer

Skewed

Question 35

A dataset with a standard deviation of 0 is:

Accepted Answer

Constant

Answer

Normally distributed

Answer

Skewed

Answer

Bimodal

Question 36

Two datasets have the same mean but different standard deviations. What can we conclude about the spread of the data in each dataset?

Accepted Answer

The dataset with the larger standard deviation has more spread around the mean.

Answer

The dataset with the larger standard deviation has a higher mean.

Answer

The datasets are identical in spread.

Question 37

The heights of 5 students (in cm) are: 160, 175, 180, 165, 170. What is the range of this dataset?

Accepted Answer

20

Answer

170

Answer

10

Answer

5

Question 38

Which measure of spread is least affected by extreme values (outliers) in a dataset?

Accepted Answer

Interquartile Range (IQR)

Answer

Variance

Answer

Range

Answer

Standard Deviation

Question 39

What is the relationship between variance and standard deviation?

Accepted Answer

Standard deviation is the square root of variance.

Answer

Variance is the square root of standard deviation.

Answer

There is no relationship between them.

Answer

They are the same thing.

Question 40

A company wants to analyze how much the number of hours its employees work each week varies. Which measure of spread would be most suitable for this purpose?

Accepted Answer

Standard Deviation

Answer

Interquartile Range

Answer

Range

Answer

Mean

Question 41

Two classes took the same test. Class A has a larger standard deviation than Class B. What does this tell us about the test scores of the two classes?

Accepted Answer

The scores in Class A were more spread out than the scores in Class B.

Answer

Class B performed better overall.

Answer

Class A performed better overall.

Question 42

The heights of 10 students in a class are recorded in centimeters: 160, 165, 170, 170, 175, 175, 180, 180, 185, 190. What is the range of these heights?

Accepted Answer

30 cm

Answer

10 cm

Answer

15 cm

Answer

175 cm

Question 43

Two data sets have the same mean. Which of these measures of spread would help us determine which set has more variability?

Accepted Answer

Standard deviation

Answer

Median

Answer

Mode

Answer

Range

Question 44

The data set 1, 2, 3, 4, 5 has a standard deviation of 1.58. If each data value is increased by 2, what will be the new standard deviation?

Accepted Answer

1.58

Answer

3.58

Answer

0.58

Answer

2.58

Question 45

Two data sets have the same range. Which of the following statements is true about their spread?

Accepted Answer

They may have different levels of spread.

Answer

The data with a lower median has more spread.

Answer

The data with a higher mean has more spread.

Answer

They have the same level of spread.

Question 46

The heights of students in two different schools are recorded. School A has a smaller standard deviation than School B. Which school has more consistent heights?

Accepted Answer

School A

Answer

School B

Answer

Both schools have the same consistency

Answer

It's impossible to determine with the information provided.

Question 47

A data set has a mean of 80 and a standard deviation of 12. If we multiply each data value by 2, what will be the new standard deviation?

Accepted Answer

24

Answer

12

Answer

48

Answer

6