Question

The mean of marks scored by $100$ students was found to be $40$. Later on, it was discovered that a score of $53$ was misread as $83$. Find the correct mean.

Answer 1

Step 1: Find the value of sum of terms

Given, the mean of $100$ students is $40$.

$\mathrm{Mean}\left(\overline{X}\right)=\frac{\mathrm{Sum}\mathrm{of}\mathrm{terms}}{\mathrm{Number}\mathrm{of}\mathrm{terms}}$

$\frac{x_1+x_2+x_3+...+x_{100}}{100}=40$

$\Rightarrow x_1+x_2+x_3+...+x_{100}=4000$

Step 2: Find the new value of sum of terms.

Sum$=x_1+x_2+x_3+...+x_{100}-83+53$

$=4000-30$

$=3970$

Step 3: Find the value of correct mean

Correct mean $\left(\overline{X}\right)=\frac{3970}{100}$

$=39.70$

Hence, the value of correct mean is $39.70$.