Question

The average of n numbers x1,x2,x3..........,xn is A.if x1 iscreplaced by (x+a)x1,x2is replaced by (x+a)x2and so on .find the new average

Answer 1

The average of n numbers = x1 + x2 + x3 ........................... xn = A

Average = sum of numbers / number of terms

              ==> ( x1 + x2 + .........................  xn ) / n = A ..............(1)

Now x1 is replaced be (x+a)x1

        x2 is replaced by (x+a)x2

        ............................... xn is replaced by (x+a)xn

Average = ( ( x + a)x1 + ( x + a )x2 + ...................... ( x + a)xn ) / n

Taking x + a as the common ;

               = ( x+a ) ( x1 + x2 + ............................ xn ) / n

               = ( x + a ) A [  see (1) ]

The average of the changed numbers is A ( x + a )

Hope it helps u :-)

Merry Christmas ^_^

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Answer 2

Answer:(x+a)*A

Step-by-step explanation:

Mean of n numbers is A

Terms are :- x1 , x2 , x3 , .............xn

We know that:-

Mean = Sum of terms ÷ Number of terms

A = (x1 + x2 + x3 + ..........xn ) ÷ n

Now ,

If all the terms are multiplied by (x+a)

New terms are :- (x+a)x1 , (x+a) x2 , (x+a) x3 ...

..........(x+a) xn

Number of terms = n

New mean = Sum of new terms ÷ number of terms

New mean =[ ( x+a)x1 , (x+a) x2 , (x+a) x3....(x+a)xn] ÷ n

Taking ( x+a ) common

New mean = (x+a) [ (x1 + x2 + x3 ....xn) ÷ n ]

As A = ( x1 + x2 + x3 ....xn ) ÷ n

So, new mean =(x+a)*A

So new mean will be (x+a)*A

Hope this will help you