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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Variance & SD MCQ & Objective Questions

Understanding Variance and Standard Deviation (SD) is crucial for students preparing for school and competitive exams. These concepts not only help in analyzing data but also play a significant role in scoring well in objective questions. Practicing MCQs and other practice questions on Variance and SD can enhance your grasp of these topics, making it easier to tackle important questions in exams.

What You Will Practise Here

Definition and significance of Variance and Standard Deviation
Formulas for calculating Variance and SD for different data sets
Understanding the relationship between Variance, SD, and data distribution
Real-life applications of Variance and SD in statistics
Common graphical representations and diagrams related to Variance and SD
Practice questions with step-by-step solutions
Tips for solving objective questions efficiently

Exam Relevance

Variance and Standard Deviation are frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require calculations, interpretations of data sets, and application of formulas. Common question patterns include direct computation of Variance and SD, as well as scenario-based questions where students must analyze data sets to derive conclusions.

Common Mistakes Students Make

Confusing Variance with Standard Deviation and vice versa
Incorrectly applying the formula for Variance, especially in grouped data
Overlooking the importance of units when interpreting results
Failing to understand the impact of outliers on Variance and SD
Misreading questions that involve multiple steps in calculations

FAQs

Question: What is the difference between Variance and Standard Deviation?
Answer: Variance measures the average of the squared differences from the mean, while Standard Deviation is the square root of Variance, providing a measure of spread in the same units as the data.

Question: How can I improve my understanding of these concepts?
Answer: Regular practice with Variance & SD MCQ questions and reviewing solved examples can significantly enhance your understanding and application skills.

Don't miss the chance to solidify your knowledge! Start solving Variance & SD practice MCQs today and boost your exam preparation. Your success is just a question away!

Variance & SD

Variance & SD MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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