Question

The average height of $10$ students in a class was calculated as $166$cm. On verification it was found that one reading was wrongly recorded as $160$cm instead of $150$cm. Find the correct mean height.

Answer 1

Here, $\overline{x}=166$cm and $n=10$
We have $\overline{x}=\frac{\sum x}{n}=\frac{\sum x}{10}$
i.e $166=\frac{\sum x}{10}$ or $\sum x=1660$
The incorrect $\sum x=1660$
The correct $\sum x=$ incorrect $\sum x-$ the wrong value $+$ correct value
$=1660-160+150=1650$
Hence, the correct A.M. $=\frac{1650}{10}=165$cm.