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Byju's Answer

Standard XII

Chemistry

Entropy

If the first ...

Question

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

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Solution

The correct option is A 0
Given $x_{i} + 5, i = 1, 2, 3, 4, 5$
Mean = $\frac{x_{1} + 5 + x_{2} + 5 + x_{3} + 5 + x_{4} + 5 + x_{5} + 5}{5}$
If $x_{i)+5,i=6,7,8,9,10$
Then mean= $\frac{x_{6} - 5 + x_{7} - 5 + x_{8} - 5 + x_{9} + 5 + x_{10} + 5}{5}$
So Net mean $\frac{x_{1} + 5 + x_{2} + 5 + x_{3} + 5 + x_{4} + 5 x_{5} + 5 + x_{6} - 5 + x_{7 - 5 + x_{8} - 5 + x_{9} - 5 + x_{10} - 5}}{10} = ¯ x$
So mean change is 0

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If the first five elements of the set x1+5,i=1,2,3...5 and the next five elements are replaced by xj−5,j=6...10 then the mean will change by

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