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Q.

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

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a

$x + n$

b

$x + (n + 1)$

c

$x + \frac{n + 1}{2}$

d

$x + \frac{n}{2}$

answer is C.

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Detailed Solution

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$\begin{array}{rcl} \begin{array}{rcl} \frac{x_{1} + x_{2} + . . . . . . + x_{n}}{n} & = & x \end{array} \\ \frac{x_{1} + 1 + x_{2} + 2 + . . . . . + x_{n} + n}{n} \\ = & \frac{x_{1} + x_{2} + . . . . . + x_{n}}{n} + \frac{1 + 2 + . . . . . . . + n}{n} \\ = & x + \frac{n (n + 1)}{2 n} \\ = & x + \frac{n + 1}{2} \end{array}$

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