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Average of ten positive numbers is $$\overline x $$. If each number is increased by 10%, then $$\overline x $$ –
- A. Remains unchanged
- B. May decrease
- C. May increase
- D. Is increased by 10%
Answer: Option D
Here is complete explanation of Average of ten positive numbers is overline x If each number….
Solution(By ExamCraze Team)
$$eqalign{
& Rightarrow frac{{{x_1} + {x_2} + ..... + {x_{10}}}}{{10}} = overline x cr
& Rightarrow {x_1} + {x_2} + ..... + {x_{10}} = 10overline x cr
& Rightarrow frac{{110}}{{100}}{x_1} + frac{{110}}{{100}}{x_2} + ..... + frac{{110}}{{100}}{x_{10}} = frac{{110}}{{100}} times 10overline x cr
& Rightarrow frac{{frac{{110}}{{100}}{x_1} + frac{{110}}{{100}}{x_2} + ..... + frac{{110}}{{100}}{x_{10}}}}{{10}} = frac{{11}}{{10}}overline x cr} $$
⇒ Average is increased by 10%
