The variance of observations $112, 116, 120, 125, 132$ is
- $58.8$
- $48.8$
- $61.8$
-
None of these
Reveal answer
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B
Correct answer
Explanation
Mean = (112+116+120+125+132)/5 = 605/5 = 121. Variance = [(112-121)^2 + (116-121)^2 + (120-121)^2 + (125-121)^2 + (132-121)^2] / 5 = (81 + 25 + 1 + 16 + 121) / 5 = 244 / 5 = 48.8.
AI explanation
To find the variance, first calculate the mean of the observations by adding them and dividing by 5, which is (112 plus 116 plus 120 plus 125 plus 132) divided by 5, giving a mean of 121. Next, find the squared deviation of each observation from this mean: 81, 25, 1, 16, and 121. The sum of these squared deviations is 244, and dividing this by 5 gives the variance of 48.8.