Question

Find the standard deviation of $10$ observations $111,211,311,...,1011$

Answer 1

The given numbers are,

$111,211,311,.....,1011$

$\Rightarrow$ $\overline{x}=\frac{111+211+311+411+511+611+711+811+911+1011}{10}=\frac{5610}{10}=561$

$\Rightarrow$ Standard deviation $=\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{10}}$

$=\sqrt{\frac{(111-561{)}^2+(211-561{)}^2+(311-561{)}^2+......+(911-561)+(1011-561{)}^2}{10}}$

$=\sqrt{\frac{(-450{)}^2+(-350{)}^2+(-250{)}^2+(-150{)}^2+(-50{)}^2+(50{)}^2+(150{)}^2+(250{)}^2+(350{)}^2+(450{)}^2}{10}}$

$=\sqrt{\frac{202500+122500+62500+22500+2500+2500+22500+62500+122500+202500}{10}}$

$=\sqrt{\frac{825000}{10}}$

$=\sqrt{82500}$

$=50\sqrt{33}$

Hence, this is the answer.