Q. 94.5( 4 Votes )

The mean of n observations is . If the first item is increased by 1, second by 2 and so on, then the new mean is
A.

B.

C.

D. None of these

Answer :

Given, mean is ,


Let x1, x2, …, xn are n observations.


And we know


The mean or average of observations, is the sum of the values of all the observations divided by the total number of observations.


i.e.



…[1]


Given as the first term is increased by 1 and 2nd term is increased by 2 and so on. Then the terms will be


x1 + 1, x2 + 2, …,xn + n


Let the new mean be x



…[2]


Now, we have series


1, 2, 3, …, n


Clearly the above series is an AP(Arithmetic progression) with


first term, a = 1 and


common difference, d = 1


And no of terms is clearly n.


And last term is also n.


We know, sum of terms of an AP if first and last terms are known is:



Putting the values in above equation we have sum of series i.e.



Using this in equation [2] and using equation [1] we have


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