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

Given:

The mean of marks scored by 100 students was found to be 40. Later on its was discovered that a score of 53 was misread as 83.

To do:

We have to find the correct mean.

Solution:

We know that,

Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$

Mean score of 100 students $= 40$

This implies,

Total score $= 100 \times 40$

$= 4000$

Difference in one score by mistake $= 83 - 53$

$= 30$

Therefore,

Correct total score $= 4000 - 30$

$= 3970$

This implies,

Correct mean $=\frac{3970}{100}$

$= 39.70$

$= 39.7$

Hence, the correct mean is 39.7.