Question

The mean of $25$ observation was found to be $78.4$. But later on it was found that $96$ was misread as $69$. The correct mean is

• A. $79.48$
• B. $76.54$
• C. $81.32$
• D. $78.4$

Answer 1

Answer: (A)

$79.48$

We know that the mean is given by $\overline{x}=\frac{\sum x}{n}\Rightarrow \sum x=n\overline{x}$
Here $\overline{x}=78.4,n=25$
$\therefore \sum x=25\times 78.4=1960$
But this $\sum x$ is incorrect as $96$ was misread as $69$.
Correct $\sum x=1960-69+96=1987$
$\therefore$ Correct mean $=\frac{1987}{25}=79.48$