JEE Main 2017 — Statistics Question with Solution

Mean $$\left(\overline{x}\right)$$ = $$\frac{x_1+x_2.....+x_n}{n}$$ = $$\frac{\sum x}{n}$$

Here, Mean = 40 of 25 teachers

$$\therefore$$ 40 = $$\frac{\sum x}{25}$$

$$\Rightarrow$$ $$\sum x$$ = 40 $$\times$$ 25 = 1000

After retireing of a 60 year old teacher, total age of 24 teachers,

x₁ + x₂ + . . . . . .x₂₄ = 1000 $$-$$ 60 = 940

Now a new teacher of age A year is appointed.

$$\therefore$$ Now total age of this 25 teachers

x₁ + x₂ + x₃ + . . . . . + x₂₅ = 940 + A

$$\therefore$$ Mean age = $$\frac{940+A}{25}$$

According to question,

$$\frac{940+A}{25}$$ = 39

$$\Rightarrow$$ A = 35