The mean of n observations is x bar

Asked by admin @ 31/08/2021 in Math viewed by 302 People

The mean of n observations is X . IF the first item is increased by 1, second by 2 and so on, then the new mean is: 1. X+n 2. X+n/2 3. X+(n+1)/2 4. X+(n-1)/2

Answered by admin @ 31/08/2021

As mean let us consider each observation is x
after every observations are increased, their sum will be nx+1+2+3+4+5+6+....…………n
that can be written as nx+sum of first n natural numbers
sum of observations =nx+n(n+1)/2
then their mean=(nx+ n(n+1)/2)/n
if we simplify the above mean=x+n+1/2
the correct answer is 3

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