# 1. Find the mean and variance for each of the data.       $\small 6, 7, 10, 12, 13, 4, 8, 12$

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

Exams
Articles
Questions