Question

Prove that if mean of the data $7,8,9,7,8,7,\lambda ,8$ is $8$ then the variance of the data $1$.

Answer 1

Arithmetic mean

$\overline{x}=\frac{x_1+x_2+x_3+.....x_n}{n}$ in case of discrete data

standard deviation

$\sigma =\sqrt{\frac{\sum {(x_i-\overline{x})}^2}{n}}$

$\overline{x}$ is mean

mean of data $\frac{7+8+9+7+8+7+2+8}{8}=8$

$n=10$

variance

$v^2=\frac{{(7-8)}^2+{(8-8)}^2+{(9-8)}^2+{(7-8)}^2+{\left(0\right)}^2+{(7-8)}^2+{(10-8)}^2+{(8-7)}^2}{8}$

$=\frac{8}{8}=1$

variance $=1$