Practice Test Discussion

The mean of n observations is $\bar{x_{1}}$ . If the first obeservation is increased by 1, second by 2 and so on, then their mean is $\bar{x_{2}}$ . The value of $\bar{x_{2}} - \bar{x_{1}}$ is?

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

$\frac{n (n + 1)}{2}$

$\frac{(n + 1)}{2}$

None of the above

Explanation

Here, new mean $\bar{x_{2}}$

$= \frac{x_{1} + x_{2} + . . . . + x_{n}}{n} + \frac{1 + 2 + 3 + . . . + n}{n} = \bar{x_{1}} + \frac{n (n + 1)}{2 n} = \bar{x_{1}} + \frac{n + 1}{2} = \bar{x_{2}} - \bar{x_{1}} = \bar{x_{1}} + \frac{n + 1}{2} - \bar{x_{1}} = \frac{n + 1}{2}$

Hence, Option A is correct

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