Question

The average of n numbers x₁, x₂, x₃ ….. x_n is A. If x₁ is replaced by  ( x+ α )x₁, x₂, is replaced by ( x+ α )x₂ and so on.
Find the new average.

Answer 1

Mean of n numbers = A
⇒ A = `[ x_1 + x_2 + ...... + x_n ]/n`

⇒ x₁ + x₂ + ............. + x_n = n x A           ......(i)
New Mean

= `[( x + a )x_1 + ( x + a )x_2 + ....... + ( x + a )x_n ]/n`

= `[ ( x + a )( x_1 + x_2 + .......... + x_n )]/n`

= `[ ( x + a )( n xx "A")]/n`             .....[ From(i) ]

= `[( x + a ) xx n xx "A" ]/n` 

= ( x + a )A