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

Average of n numbers = A

⇒ A = $\dfrac{x$1 + x2 + x3 + ……. + xn}{n}

⇒ $x$1 + x2 + x3 + ……. + xn = nA ……….(1)

New average = $\dfrac{(x + a)x$1 + (x + a)x2 + (x + a)x3 + ……. + (x + a)xn}{n}

= $\dfrac{(x + a)(x$1 + x2 + x3 + ……. + xn)}{n}

= $\dfrac{(x + a)(nA)}{n}$ [∵Using equation (1)]

= $(x + a)A$

Hence, new average is (x + a)A.