Q. A data set has values: 10, 12, 14, 16. What is the variance? (2021)
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. Calculate the variance for the following data: 2, 4, 4, 4, 5, 5, 7, 9. (2019)
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)
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. For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)
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: 3, 3, 3, 3, 3, what is the variance? (2023)
Solution
All values are the same, so variance = 0.
Correct Answer: A — 0
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Q. If the data set is: 5, 5, 5, 5, what is the variance? (2019)
Solution
All values are the same, so variance = 0.
Correct Answer: A — 0
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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)
Solution
Standard deviation is the square root of variance. Therefore, SD = √25 = 5.
Correct Answer: B — 10
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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)
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)
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)
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)
Solution
Standard deviation is the square root of variance. Therefore, SD = √25 = 5.
Correct Answer: A — 5
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Q. The mean of a data set is 10 and the variance is 4. What is the standard deviation? (2019)
Solution
Standard deviation is the square root of variance. Therefore, SD = √4 = 2.
Correct Answer: A — 2
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Q. The scores of a test are: 20, 30, 40, 50. What is the standard deviation? (2020)
Solution
Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).
Correct Answer: B — 15
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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)
Solution
Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8. SD = √8 = 2.83 (approximately 3).
Correct Answer: A — 2
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Q. The scores of five students are: 20, 22, 24, 26, 28. What is the variance? (2020)
Solution
Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8.
Correct Answer: A — 4
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Q. The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)
Solution
Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.
Correct Answer: B — 5
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Q. What is the variance of the following numbers: 1, 2, 3, 4, 5, 6? (2022)
-
A.
2.5
-
B.
3.5
-
C.
4.5
-
D.
5.5
Solution
Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. Variance = [(1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²] / 6 = 2.92 (approx 2.5).
Correct Answer: A — 2.5
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Q. What is the variance of the numbers: 1, 1, 1, 1, 1? (2023)
Solution
All values are the same, so variance = 0.
Correct Answer: A — 0
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Q. What is the variance of the numbers: 5, 5, 5, 5? (2023)
Solution
All values are the same, so variance = 0.
Correct Answer: A — 0
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