Average of ten positive numbers is `overline(x)`. If each number is increased by 10 %, then `overline(x)` Options: A . &nbspremains unchanged B . &nbspmay decrease C . &nbspmy increase D . &nbspis increased by 10%

Average of ten positiv

Question

Average of ten positive numbers is `overline(x)`. If each number is increased by 10 %, then `overline(x)`

Options:

A . remains unchanged

B . may decrease

C . my increase

D . is increased by 10%

Answer: Option D

`(x_1 + x_2 + .......................+ x_10)/(10)` = `overline(x)` `hArr` `x_1 + x_2 +...................+x_10` = `10overline(x)`

`hArr` `110/100 x_1 + 110/100 x_2+................+110/100 x_10 ` = `110/100 ` x `10overline(x)`

`hArr` `110/100 x_1 + 110/100 x_2+................+110/100 x_10 ` = `11/10 ` x `10overline(x)`

___________________________________________

`hArr` Average is increased by 10%

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