Question
The mean of n items is ¯¯¯x. If the first term is increased by 1 second by 2 and so on, then new mean is
Answer: Option C
:
C
Let, x1,x2.......xn be n items.
Then, ¯¯¯x=1n∑xi
Lety1=x1+1,y2=x2+2,y3=x3+3,.....,yn=xn+n
Then the mean of the new series is
1n∑yi=1nn∑i=1(xi+i)
=1nn∑i=1xi+1n(1+2+3+......+n)
=¯¯¯x+1n.n(n+1)2=¯¯¯x+n+12
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:
C
Let, x1,x2.......xn be n items.
Then, ¯¯¯x=1n∑xi
Lety1=x1+1,y2=x2+2,y3=x3+3,.....,yn=xn+n
Then the mean of the new series is
1n∑yi=1nn∑i=1(xi+i)
=1nn∑i=1xi+1n(1+2+3+......+n)
=¯¯¯x+1n.n(n+1)2=¯¯¯x+n+12
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