What is the variance of the largest five observations ?
Consider the following for the next two (02) items that follow : The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41.
- A. 14.6
- B. 21.8
- C. 25.2
- D. 46.8 ✓
Correct Answer: D. 46.8
Explanation
The largest five observations are 32, 35, 41, 47, 50, with mean \bar{x} = 41. The squared deviations are (32-41)^2=81, (35-41)^2=36, (41-41)^2=0, (47-41)^2=36, and (50-41)^2=81. The variance is the average of these squared deviations: \sigma^2 = \frac{81 + 36 + 0 + 36 + 81}{5} = \frac{234}{5} = 46.8.
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