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Question

If the mean of the set of numbers $$x_1, x_2, x_3,\cdots x_n$$ is $$\bar{x}$$ then the mean of numbers $$x_i+2i$$
$$\forall i=1, 2, 3,\cdots n$$ such that $$1\leq i\leq n,$$ is


A
¯x+n
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B
¯x+n+1
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C
¯x+2
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D
¯x+2n
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Solution

The correct option is A $$\bar{x}+n+1$$
Required mean $$=\displaystyle \frac{\sum_{i=1}^{i=n} \left(x_i+2i\right)}{n}=\frac{\sum x_i}{n}+2.\frac{\sum n }{n}=\bar{x}+n+1$$

Mathematics

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