# Average of ten positive numbers is overline x If each number…

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### Average of ten positive numbers is $$\overline x$$. If each number is increased by 10%, then $$\overline x$$ –

1. A. Remains unchanged
2. B. May decrease
3. C. May increase
4. D. Is increased by 10%

eqalign{ & Rightarrow frac{{{x_1} + {x_2} + ..... + {x_{10}}}}{{10}} = overline x cr & Rightarrow {x_1} + {x_2} + ..... + {x_{10}} = 10overline x cr & Rightarrow frac{{110}}{{100}}{x_1} + frac{{110}}{{100}}{x_2} + ..... + frac{{110}}{{100}}{x_{10}} = frac{{110}}{{100}} times 10overline x cr & Rightarrow frac{{frac{{110}}{{100}}{x_1} + frac{{110}}{{100}}{x_2} + ..... + frac{{110}}{{100}}{x_{10}}}}{{10}} = frac{{11}}{{10}}overline x cr}