Question

Average of ten positive numbers is x.If each number is increased by 12% then x is incresed by

Answer 1

Hi there!
Here's the answer :

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$Average = \frac{Sum\: of\: Observations}{No.\: of\: Observations}$

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If a No. x is increased by 12%
No. after %Increase => x + (12% of x)
= x + (12/100)x
= x + 0.12x
= 1.12x

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SOLUTION:

Given,
No. of observations = 10

Let 10 numbers be x1, x2, x3, …… , x10

As per given data,
Average of these No.s = x

$x= \frac{x1 + x2 + x3 + …… + x10}{10}$ ---------(1)

If the each No. is increased by 10%, then New Average be y

=> $y = \frac{1.12 x1 + 1.12 x2 + 1.12 x3 + …… + 1.12 x10}{10}$

=> $y = 1.12 × (\frac{x1 + x2 + x3 + …… + x10}{10})$

From eq(1) ,

=> $y = 1.12 × x$

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$\underline{\underline{x\: is\: 12\%\: Increased}}$

Conclusion :
If each of n observation in an average is increased by k%, then new average increases by k%.

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Hope it helps