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

If initially all marks were $x_i$, then
${\sigma }_1^2=\frac{\sum (x_i-\overline{x}{)}^2}{N}$
Now, each is increased by 10.
$\therefore {\sigma }_2^2=\frac{\sum \left[\right(x_i+10)-(\overline{x}-10){]}^2}{N}={\sigma }_1^2$
So, variance will not change whereas mean, median and mode will increase by 10.