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Question

The mean of n items is ¯x If the first item is increased by 1, second by 2 and so on, then the new mean is

A
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C
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Solution

The correct option is C
Let x1,x2,....xn be n itemsThen ¯x=1nxiLet y1=x1+1,y2=x2+2,y3=x3+3,yn=xn+nThen the mean of the new series is1nyi=12(xi+i)=1nxi+1n(1+2+3+....+n)=¯X+1n,n(n+1)2=¯x+n+12

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