QJEEM13Ma574c: JEE Main 2013 Mathematics - Class 11 JEEM13Ma574c Solution: All the students of a class performed poorly in Mathematics.…

As we know variance does not change with the change of origin. So, here even after adding grace marks $$10$$, the variance will be same.

Let's see with an example,

Assume initial variance $$=\frac{\sum {\left(x_i-\bar{x}\right)}^2}{N}$$

After adding grace marks $$10$$ with each student,

the final variance $$={\frac{\sum \left[\left(x_i+10\right)-\left(\bar{x}+10\right)\right]}{N}}^2$$

$$=\frac{\sum {\left(x_i-\bar{x}\right)}^2}{N}$$

$$=$$ Initial variance.