if the first five elements of the set $x_{1}, x_{2} . . . . . x_{10}$ are replaced by $x_{i} + 5, i = 1, 2, 3, 4, 5$ and next five elements are replaced by $x_{i} - 5, j = 6, 7......10,$ then the mean will change by?

0

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\frac{n + 1}{2}

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10

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25

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Solution

The correct option is B $0$
Let $¯ ¯¯¯ ¯ X = \frac{x_{1} + x_{2} + x_{3} + . . . . + x_{10}}{10}$
New mean $= \frac{(x_{1} + 5) + (x_{2} + 5) . . . + (x_{6} - 5) + (x_{7} - 5) . . . + (x_{10} - 5)}{10}$
$= \frac{x_{1} + x_{2} + x_{3} + . . . . + x_{10}}{10} = ¯ ¯ ¯ x$
So the mean will change by 0

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