Question:

If both the mean and the standard deviation of 50 observations x_1, x_2,......, x_50 are equal to 16, then the mean of (x_1 - 4)^2, (x_2 - 4)^2,.....(x_50 - 4)^2 is:

525

480

400

380

Correct option is D.400Mean(μ)=∑xi50=16standard deviation(σ)=∑xi250−(μ)2=16⇒(256)×2=∑xi250New mean=∑(xi−4)250=∑xi2+16×50−8∑xi50=(256)×2=16−8×16=