JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Statistics

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by

p

and then reduced by

q

, where

p \neq = 0

and

q \neq = 0

. If the new mean and new s.d. become half of their original values, then

q

is equal to:

Answer: (D)

Solution

Multiplying each observation by

p

and subtracting

q

turns the mean into

p \overset{x}{ˉ} - q

and the standard deviation into

∣ p ∣ σ

. Halving both gives

10 = 20 p - q

and

1 = 2∣ p ∣

, so

∣ p ∣ = \frac{1}{2}

. Taking

p = \frac{1}{2}

would force

q = 0

, which is excluded, so

p = - \frac{1}{2}

, and then

10 = - 10 - q

gives

q = - 20

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Single correct option