Question

The arithmetic mean of a group of $75$ observations was calculated as $27$. It was later found that one observation was wrongly read as $43$ instead of the correct value $53$. Obtain the correct arithmetic mean of the data.

Answer 1

Number of observations= $75$

Mean=$27$

Sum of observations=$75\times 27$

Wrong value=$43$, Correct value=$53$

$\therefore$Correct sum=$75\times 27-43+53=75\times 27+10$

Correct mean=$\frac{75\times 27+10}{75}=27+\frac{10}{75}=27.133$