$T h e m e a n o f n i t e m s i s ¯ x I f t h e f i r s t i t e m i s i n c r e a s e d b y 1, s e c o n d b y 2 a n d s o o n, t h e n t h e n e w m e a n i s$

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Solution

The correct option is C
$L e t x_{1}, x_{2}, . . . . x_{n} b e n i t e m s T h e n ¯ x = \frac{1}{n} \sum x_{i} L e t y_{1} = x_{1} + 1, y_{2} = x_{2} + 2, y_{3} = x_{3} + 3, y_{n} = x_{n} + n T h e n t h e m e a n o f t h e n e w s e r i e s i s \frac{1}{n} \sum y_{i} = \frac{1}{2} \sum (x_{i} + i) = \frac{1}{n} \sum x_{i} + \frac{1}{n} (1 + 2 + 3 + . . . . + n) = ¯ X + \frac{1}{n}, \frac{n (n + 1)}{2} = ¯ x + \frac{n + 1}{2}$

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