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. 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. 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 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 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. 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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