The mean of the marks scored by 50 students was found to be 39
Question:

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean.

Solution:

Let the marks scored by 50 students be x1x2,…x50.
Mean = 39
We know:

Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$

Thus, we have:

$39=\frac{x_{1}+x_{2}+\ldots+x_{50}}{50}$

$\Rightarrow x$

$\Rightarrow x_{1}+x_{2}+\ldots+x_{50}=1950 \ldots \ldots$ (i)

Also, a score of 43 was misread as 23.

$\therefore$ New Mean $=\frac{\left(x_{1}+x_{2}+\ldots+x_{50}\right)-23+43}{50}$

$=\frac{1950-23+43}{50} \quad[$ using $(\mathrm{i})]$

$=\frac{1970}{50}$

$=39.4$