Question

The mean of the $5$ numbers is $32$. If one of the numbers is excluded, then the mean is reduced by $4$. Find the excluded number.

Answer 1

Mean of $5$ numbers $=32$.
Sum of these numbers $=32\times 5=160$ $(\because n\overline{x}=\sum x)$
Mean of $4$ numbers $=32-4=28$
Sum of these $4$ numbers $=28\times 4=112$
Excluded number $=$ (Sum of the $5$ given numbers) $-$ (Sum of the $4$ numbers)
$=160-112=48$