Question

The mean of $100$ items was found to be $64$. Later on, it was discovered that two items were misread as $26$ and $9$ instead of $36$ and $90$ respectively. Find the correct mean.

Answer 1

Step 1: Find the value of sum of terms

Given, the mean of $100$ items is $64$.

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

$\frac{x_1+x_2+x_3+...+x_{100}}{100}=64$

$\Rightarrow x_1+x_2+x_3+...+x_{100}=6400$

Step 2: Find the new value of sum of terms

$Sum=x_1+x_2+x_3+...+x_{100}-26-9+36+90$

$=6400-26-9+36+90$

$=6491$

Step 3: Find the value of correct mean

Correct mean $\left(\overline{X}\right)=\frac{6491}{100}$

$=64.91$

Hence, the value of correct mean is $64.91$.