Question

Compute the standard deviation for the set of data. 2, 4, 6, 8, 10

Answer 1

$\sigma$ - standard deviation
m - mean
$\sigma= \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i-m)^2} \\m= \frac{2+4+6+8+10}{5}= \frac{30}{5} =6 \\ \\ \sigma= \sqrt{ \frac{1}{5} \sum_{i=1}^{5} (x_i-6)^2} \\= \sqrt{ \frac{1}{5} [ (2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2]} \\= \sqrt{ \frac{1}{5} [ 16+4+0+4+16]} \\= \sqrt{ \frac{1}{5} \times 40} \\= \sqrt{ \frac{1}{5} \times 40} \\=2\sqrt{2}$

Answer 2

6 is the correct anwser