Question

The mean of n observations is x. If the first item is increased by 1,second by 2 and so on....FIND THE NEW MEAN

Answer 1

Let x1,x2,...xn are n observations

Mean =(x1+x2+...xn)/n=x----(1)

If new observations are

x1+1,x2+2,...xn+n

New mean =[(x1+1)+(x2+2)+...+(xn+n)]/n

=(x1+x2+...+xn)/n + (1+2+...+n)/n

 

=x+[n(n+1)/2n]

=x+(n+1)/2

 

Hope This Helps :)