Question

All students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

• A. mean
• B. median
• C. mode
• D. variance

Answer 1

The correct option is D variance

As we know, mean, median and mode will increase by $10$
Now check the variance,
Variance $={\sigma }^2=\frac{\sum (x_i-\overline{x}{)}^2}{N}$
Now increase the $x_i$ and $\overline{x}$ by $10$
$\Rightarrow {\sigma }^2=\frac{\sum {\left[\right(x_i+10)-(\overline{x}+10\left)\right]}^2}{N}$
$\Rightarrow {\sigma }^2=\frac{\sum (x_i-\overline{x}{)}^2}{N}$
Hence, variance is same