Answer-first summary for fast verification
Answer: 0.00160
The unbiased estimator for the sample variance is calculated using the formula \( s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \mu)^2 \), where \( n \) is the sample size and \( \mu \) is the sample mean. From the table provided, the sample mean \( \mu \) is calculated as \( \frac{21\% + 17\% + 11\% + 18\% + 13\%}{5} = 16\% \). Substituting the values into the formula, we get: \[ s^2 = \frac{(21\% - 16\%)^2 + (17\% - 16\%)^2 + (11\% - 16\%)^2 + (18\% - 16\%)^2 + (13\% - 16\%)^2}{5 - 1} \] \[ s^2 = \frac{(5\%)^2 + (1\%)^2 + (-5\%)^2 + (2\%)^2 + (-3\%)^2}{4} \] \[ s^2 = \frac{25\% + 1\% + 25\% + 4\% + 9\%}{4} \] \[ s^2 = \frac{64\%}{4} \] \[ s^2 = 0.0160 \] or \[ s^2 = 0.00160 \] This calculation leads us to the correct answer, which is option B: 0.00160. This is the unbiased sample variance of the returns data.
Author: LeetQuiz Editorial Team
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As the Chief Investment Officer (CIO) of a global macro fund, you are tasked with assessing the performance of various international portfolio managers within your fund. You have compiled the following data on the annualized total returns for each manager:
| Portfolio Manager | Annualized Total Return |
|---|---|
| Manager 1 | 21% |
| Manager 2 | 17% |
| Manager 3 | 11% |
| Manager 4 | 18% |
| Manager 5 | 13% |
Your objective is to calculate the unbiased sample variance for the annualized total returns presented in the table.
A
0.00128
B
0.00160
C
0.00288
D
0.00360
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