Multiple choice

The variance of observations 8, 12, 13, 15, 22, is

  1. 21

  2. 21.2

  3. 21.4

  4. None of these
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B Correct answer
Explanation

Mean = (8+12+13+15+22)/5 = 70/5 = 14. Variance = [(8-14)^2 + (12-14)^2 + (13-14)^2 + (15-14)^2 + (22-14)^2] / 5 = (36 + 4 + 1 + 1 + 64) / 5 = 106 / 5 = 21.2.

AI explanation

First, calculate the mean of the observations by dividing the sum 70 by the total count 5, which gives 14. Next, find the squared deviations from this mean: 36, 4, 1, 1, and 64. The sum of these squared deviations is 106. Divide this sum by the total number of observations 5 to obtain the variance of 21.2.

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