Question

if x is the arithmetic mean of n observations x1 x2,........, xn, then find the arithmetic mean of x1 + a, x2 + a, , xn + a.

Answer 1

Answer:

x + a

Step-by-step explanation:

Given that x is the arithmetic mean of x₁, x₂, ..., xₙ ; that is:

x = ( x₁+ x₂+...+ xₙ ) / n

Then the arithmetic mean of x₁+a, x₂+a, ..., xₙ+a is

( (x₁+a) + (x₂+a) +...+ (xₙ+a) ) / n

= ( ((x₁+ x₂+...+ xₙ) + na ) / n

= ( x₁+ x₂+...+ xₙ ) / n  +  a

= x + a

Answer 2

mark this answer as Brainlist