Question

If both the means and the standard deviation of 50 observations x₁, x₂, ………, x₅₀ are equal to 16, then the mean of (x₁ - 4)², (x₂ - 4)², …., (x₅₀ - 4)²
is (A) 400 (B) 380
(C) 525 (D) 480

Answer 1

The mean of the (x₁ - 4)², (x₂ - 4)², …., (x₅₀ - 4)² is 400

1.mean=Σxi/50=16( formula for mean)

2.standard deviation=16(given value of standard deviation)

3.

variance=256

4.variance remains same

5.

σ^2=1/50 Σ(xi-4)^2-(16-4)^2=256

1/50Σ(xi-4)^2=144+256=400

mean=Σ(xi-4)^2/50 which is equal to 400