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  • Find the mean and variance for each of the data. (1) 6, 7, 10, 12, 13, 4, 8, 12

1. Find the mean and variance for each of the data.

       \small 6, 7, 10, 12, 13, 4, 8, 12

Answers (1)

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Mean (\overline{x}) of the given data:

\overline{x} = \frac{1}{8}\sum_{i=1}^{8}x_i = \frac{6+ 7+ 10+ 12+ 13+ 4+ 8+ 12}{8} = \frac{72}{8} = 9

The respective values of the deviations from mean, (x_i - \overline{x}) are

-3, -2, 1 3 4 -5 -1 3

\therefore  \sum_{i=1}^{8}(x_i - 10)^2 = 74

\therefore \sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \overline{x})^2

\frac{1}{8}\sum_{i=1}^{8}(x_i - \overline{x})^2= \frac{74}{8} = 9.25

Hence,  Mean = 9 and Variance = 9.25

Posted by

HARSH KANKARIA

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