# 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 statistical measure will not change even after the grace marks were given ?

## 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 statistical measure will not change even after the grace marks were given ?

(a) Mean

(b) Median

(c) Mode

(d) Variance

## Solution :

If initially all marks were given $$x_i$$, then

$${\sigma_i}^2$$ = $$\sum(x_i – \bar{x})^2\over N$$

Now, each is increased by 10.

$$\therefore$$ $${\sigma_i}^2$$ = $$\sum((x_i + 10) – (\bar{x} + 10))^2\over N$$

= $${\sigma_i}^2$$

So, variance will not change whereas mean, median and mode will increase by 10.

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