Variance & SD: Essential Concepts for Competitive Exams

Variance & SD

Q. A data set has a mean of 20 and a variance of 16. What is the range of the data if it is normally distributed? (2023)

A. 8
B. 16
C. 32
D. 64

Solution

In a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean. SD = √16 = 4. Range = 20 ± 2*4 = 20 ± 8 = 12 to 28.

Correct Answer: C — 32

Learn More →

Q. A data set has a mean of 20 and a variance of 16. What is the range of the data if the maximum value is 28? (2023)

A. 8
B. 12
C. 16
D. 20

Solution

If the variance is 16, the standard deviation is 4. The minimum value can be calculated as 20 - 4 = 16. Therefore, range = 28 - 16 = 12.

Correct Answer: B — 12

Learn More →

Q. A data set has a mean of 50 and a variance of 25. What is the standard deviation? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Correct Answer: B — 10

Learn More →

Q. A data set has values: 10, 12, 14, 16. What is the variance? (2021)

A. 2
B. 4
C. 6
D. 8

Solution

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.

Correct Answer: B — 4

Learn More →

Q. A data set has values: 2, 4, 4, 4, 5, 5, 7, 9. What is the variance? (2021)

A. 4
B. 5
C. 6
D. 7

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 5.

Correct Answer: B — 5

Learn More →

Q. A set of numbers has a variance of 36. What is the standard deviation? (2019)

A. 6
B. 12
C. 18
D. 24

Solution

Standard deviation is the square root of variance. Therefore, SD = √36 = 6.

Correct Answer: A — 6

Learn More →

Q. Calculate the variance for the following data: 2, 4, 4, 4, 5, 5, 7, 9. (2019)

A. 4
B. 5
C. 6
D. 7

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 5

Learn More →

Q. Calculate the variance for the following data: 3, 7, 7, 19. (2022)

A. 20
B. 25
C. 30
D. 35

Solution

Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.

Correct Answer: B — 25

Learn More →

Q. Calculate the variance for the following data: 5, 7, 9, 11. (2022)

A. 2.5
B. 3.5
C. 4.0
D. 5.0

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.

Correct Answer: B — 3.5

Learn More →

Q. Calculate the variance of the following numbers: 1, 2, 3, 4, 5. (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

Learn More →

Q. For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

Learn More →

Q. For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)

A. 8
B. 10
C. 12
D. 14

Solution

Mean = (10 + 12 + 14 + 16 + 18) / 5 = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.

Correct Answer: A — 8

Learn More →

Q. For the data set: 10, 12, 14, 16, what is the variance? (2019)

A. 2
B. 4
C. 6
D. 8

Solution

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.

Correct Answer: B — 4

Learn More →

Q. For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)

A. 6
B. 8
C. 10
D. 12

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6. Variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²] / 5 = 8.

Correct Answer: A — 6

Learn More →

Q. For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

Learn More →

Q. For the data set: 5, 7, 9, 11, 13, what is the variance?

A. 4
B. 6
C. 8
D. 10

Solution

Mean = 9. Variance = [(5-9)² + (7-9)² + (9-9)² + (11-9)² + (13-9)²] / 5 = 8.

Correct Answer: A — 4

Learn More →

Q. If the data set is: 2, 4, 4, 4, 5, 5, 7, 9, what is the variance? (2022)

A. 4
B. 5
C. 6
D. 7

Solution

Mean = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: C — 6

Learn More →

Q. If the data set is: 5, 5, 5, 5, what is the variance? (2019)

A. 0
B. 1
C. 2
D. 5

Solution

All values are the same, so variance = 0.

Correct Answer: A — 0

Learn More →

Q. If the data set is: 5, 7, 9, 11, what is the variance? (2022)

A. 2
B. 3
C. 4
D. 5

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 5.

Correct Answer: A — 2

Learn More →

Q. If the mean of a data set is 15 and the standard deviation is 5, what is the variance? (2022)

A. 10
B. 15
C. 20
D. 25

Solution

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Correct Answer: D — 25

Learn More →

Q. If the mean of a data set is 20 and the standard deviation is 5, what is the variance?

A. 10
B. 15
C. 20
D. 25

Solution

Variance = (Standard Deviation)² = 5² = 25.

Correct Answer: D — 25

Learn More →

Q. If the mean of a data set is 30 and the standard deviation is 5, what is the variance? (2023)

A. 10
B. 15
C. 20
D. 25

Solution

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Correct Answer: D — 25

Learn More →

Q. If the mean of a data set is 50 and the standard deviation is 10, what is the variance? (2023)

A. 50
B. 100
C. 150
D. 200

Solution

Variance is the square of the standard deviation. Therefore, variance = 10² = 100.

Correct Answer: B — 100

Learn More →

Q. If the mean of a data set is 50 and the variance is 25, what is the standard deviation? (2019)

A. 5
B. 10
C. 15
D. 20

Solution

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Correct Answer: B — 10

Learn More →

Q. If the standard deviation of a population is 7, what is the variance? (2022)

A. 14
B. 21
C. 49
D. 56

Solution

Variance is the square of the standard deviation. Therefore, variance = 7² = 49.

Correct Answer: C — 49

Learn More →

Q. If the standard deviation of a set of numbers is 3, what is the variance? (2020)

A. 6
B. 9
C. 12
D. 15

Solution

Variance is the square of the standard deviation. Therefore, variance = 3² = 9.

Correct Answer: B — 9

Learn More →

Q. If the variance of a data set is 16, what is the range of the data if the minimum value is 0? (2023)

A. 8
B. 16
C. 4
D. 12

Solution

Standard deviation = √16 = 4. If the minimum is 0, the maximum can be 4, thus range = 4 - 0 = 4.

Correct Answer: A — 8

Learn More →

Q. If the variance of a population is 16, what is the standard deviation? (2023)

A. 4
B. 8
C. 16
D. 2

Solution

Standard deviation is the square root of variance. Therefore, SD = √16 = 4.

Correct Answer: A — 4

Learn More →

Q. If the variance of a population is 25, what is the standard deviation? (2022)

A. 5
B. 10
C. 15
D. 20

Solution

Standard deviation = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. If the variance of a sample is 25, what is the standard deviation? (2023)

A. 5
B. 10
C. 15
D. 20

Solution

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Correct Answer: A — 5

Learn More →

Showing 1 to 30 of 49 (2 Pages)

Variance & SD

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?