The mean of `n` observations is ` X ` . If the first item is increased by 1, second by 2 and so on, then the new mean is (a) ` X +n` (b) ` X +n/2` (c) ` X +(n+1)/2` (d) None of these

Options

A. `overline(X) +n`
B. `overline(X)+(n)/(2)`
C. `overline(X)+(n+1)/(2)`
D. None of these

Explanation

Mean of` x_1, x_2, \ldots\ x_n is x`


`frac{x_1+x_2+x_3+\ldots\+x_n}{n}=x `


`Rightarrow sum_{i=1}^{n} x=n x \ldots\(1)`


` add 1` to `x_1`, `2 to x_2` and so on


`x_1+1+x_}+2+\ldots\+x_n+n`


`=(x_1+x_2+ldots+x_n)+(1+2+ldots+n) `


`=sum n+frac{n(n+1)}{2}`


`New mean =frac{text { New summation }}{n}`


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