If average of 20 observations x1,x2, ....., x20 is y, then the average of x1 &nd

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If average of 20 observations x₁,x₂, ....., x₂₀ is y, then the average of x₁ – 101, x₂ – 101, x₃ –101, ....., x₂₀ –101 is

Options:

A . y-20

B . y-101

C . 20y

D . 101y

Answer: Option B
Answer: (b)
${X_1 + X_2 + X_3 + X_4 + ..... + X_20}/20 = Y$
$X_1 + X_2 + X_3 + X_4 + ..... + X_20 = 20Y$
$= {X_1 - 101 + X_2 - 101 + X_3 - 101 + X_4 - 101 + ..... + X_20 - 101}/20$
$= (X_1 + X_2 + X_3 + X_4 + ..... + X_20) - 20 x 101/20$
$\text"20Y - 20 x 101"/20$
= Y - 101

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