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

Answer: (D)

Variance

Answer 2

If initially all m arks were $x_i,$ then
$\sigma_1^2 = \frac{ \sum \, ( x_i - \overline{ x} )^2 }{ N}$
Now, each is increased by 10
$\therefore \sigma_1^2 = \frac{ \sum [ ( x_i + 10 ) - ( \overline{ x} + 10)]^2 }{ N} = \sigma_1^2$
So, variance will not change whereas mean, median and
mode will increase by 10.