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Q.

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

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a

$\bar{x} + n$

b

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

c

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

d

$\bar{x} + (n + 1)$

answer is C.

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Detailed Solution

$\begin{array}{l} \bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n}, {\bar{x}}_{1} = \frac{\sum_{i = 1}^{n} x_{i} + (1 + 2 + \dots \dots + n)}{n} = \bar{x} + \frac{\frac{n (n + 1)}{2}}{n} \\ \Rightarrow {\vec{x}}_{1} = {\bar{x}}_{1} + \frac{n + 1}{2} \end{array}$

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