Question:
The mean and variance of \( n \) observations are 8 and 16, respectively. If the sum of the first \( (n-1) \) observations is 48 and the sum of squares of the first \( (n-1) \) observations is 496, then the value of \( n \) is:
The mean and variance of \( n \) observations are 8 and 16, respectively. If the sum of the first \( (n-1) \) observations is 48 and the sum of squares of the first \( (n-1) \) observations is 496, then the value of \( n \) is:
Updated On: Apr 10, 2026
- 21
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- 13
- 7
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The Correct Option is C
Solution and Explanation
Given that the mean is 8 and the variance is 16, we know the following:
- Mean: \( \frac{\text{sum of observations}}{n} = 8 \)
- Variance: \( \frac{\text{sum of squares of observations}}{n} - \left(\frac{\text{sum of observations}}{n}\right)^2 = 16 \) We also know the sum of the first \( (n-1) \) observations is 48, and the sum of squares of the first \( (n-1) \) observations is 496. Now, using these formulas, we can calculate the value of \( n \) as 13.
Final Answer: 13
- Variance: \( \frac{\text{sum of squares of observations}}{n} - \left(\frac{\text{sum of observations}}{n}\right)^2 = 16 \) We also know the sum of the first \( (n-1) \) observations is 48, and the sum of squares of the first \( (n-1) \) observations is 496. Now, using these formulas, we can calculate the value of \( n \) as 13.
Final Answer: 13
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