Question

Arithmetic mean of $9$ observations was calculated as $45$. In doing so an observation was wrongly taken as $42$ for $24$. What would then be the correct mean?

Answer 1

$Mean$ of $9$ observation $=45.$

$\overline{x}=45$

$n=9$

$\overline{x}=\frac{\sum x}{n}$

$\sum x=\overline{x}n=45\times 9=405$

Sum of all observation are $405.$

Now an observation was wrongly taken as $42$ for $24.$

$\therefore$ $42-24=18$ was mistakely added more.

$\therefore$ $\sum x-18=387=\sum y$ [the correct sum of all observation.]

$\therefore \overline{y}=\frac{\sum y}{n}=\frac{387}{9}=43$

$\therefore 43$ is the correct mean.