If the first item is increased by 1, second by 2 and so on, then the new mean is

# If the first item is increased by 1, second by 2 and so on, then the new mean is

1. A

$\overline{X}+n$

2. B

$\overline{X}+\frac{n}{2}$

3. C

$\overline{X}+\frac{n+1}{2}$

4. D

none of these

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### Solution:

Let ${x}_{1},{x}_{2},\dots ,{x}_{n}$ be n values of variable X. Then

$\overline{X}=\frac{1}{n}\mathrm{\Sigma }{x}_{i}$

Let ${y}_{1}={x}_{1}+1,{y}_{2}={x}_{2}+2,{y}_{3}={x}_{3}+3,\dots ,{y}_{n}={x}_{n}+n$ Then the mean of the new series is given by

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