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

Answer 1

Answer: (C)

variance

Answer 2

Variance doesn't change with the change of origin.
$\sigma_1^2 = \frac{1}{n} \sum(x_i - \bar{x} )^2$
$\sigma_2^2 = \frac{1}{n} \sum \\{(x_i + 10) -(\bar{x} + 10)\\}^2$
Hence $\sigma_1^2 = \sigma_2^2$