Question

calculate variance of 6,80,10,12,14.​

Answer 1

$\textbf{Given:}$

$\text{Numbers are 6,80,10,12,14}$

$\textbf{To find:}$

$\text{Variance of the given set of values}$

$\textbf{Solution:}$

$\text{First we find mean of the given set of values}$

$\textbf{Mean}$

$\overline{x}=\dfrac{{\sum}\;x_i}{n}$

$=\dfrac{x_1+x_2+x_3+x_4+x_5}{5}$

$=\dfrac{6+80+10+12+14}{5}$

$=\dfrac{122}{5}$

$=24.4$

$\textbf{Variance}$

$=\dfrac{{\sum}(x_i-\overline{x})^2}{n}$

$=\dfrac{(6-24.4)^2+(80-24.4)^2+(10-24.4)^2+(12-24.4)^2+(14-24.4)^2}{5}$

$=\dfrac{(-18.4)^2+(55.6)^2+(-14.4)^2+(-12.4)^2+(-10.4)^2}{5}$

$=\dfrac{3,899.2}{5}$

$=779.84$

$\textbf{Answer:}$

$\textbf{Variance is 779.84}$