Question

All the 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

Explanation for the correct option:

If initially all marks were $x_i$​, then

${{\sigma }_i}^2=\frac{\sum {(x_i-\overline{x})}^2}{N}$

Now, each student marks is increased by $10$

$\begin{array}{rcl}\therefore {{\sigma }_i}^2& =& \frac{\sum {\left[\right(x_i+10)-(\overline{x}+10\left)\right]}^2}{N}\\ & =& {{\sigma }_i}^2\end{array}$

Thus, variance will not change whereas mean, median and mode will increase by $10$

Hence, Option ‘D’ is Correct.