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Question
The average of n numbers x1, x2, x3 ….. xn is A. If x1 is replaced by ( x+ α )x1, x2, is replaced by ( x+ α )x2 and so on.
Find the new average.
Solution
Mean of n numbers = A
⇒ A = `[ x_1 + x_2 + ...... + x_n ]/n`
⇒ x1 + x2 + ............. + xn = 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
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