Question

Find the variance and standard deviation of the following data 5,12,3,18,6,8,2,10

Answer 1

Arranging given number in ascending order,

$2,3,5,6,8,10,12,18$

$Mean\left(\overline{x}\right)=\frac{2+3+5+6+8+10+12+18}{8}$

$=\frac{64}{8}=8$

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

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

$Variance\left({\sigma }^2\right)=\frac{(2-8{)}^2+(3-8{)}^2+(5-8{)}^2+(6-8{)}^2+(8-8{)}^2+(10-8{)}^2+(12-8{)}^2+(18-8{)}^2}{8}$

$=\frac{(-6{)}^2+(-5{)}^2+(-3{)}^2+(-2{)}^2+(0{)}^2+(2{)}^2+(4{)}^2+(8{)}^2}{8}$

$=\frac{36+25+9+4+0+4+16+64}{8}$

$=\frac{158}{8}$

$=19.75$

$Standarddeviation\left(\sigma \right)=\sqrt{19.75}$

$=4.44$

Hence, this is the answer.