Question

Average of five numbers is 20. If each number is multiplied by 2, what will be the new average?

Answer 1

10

average is 20

lets say 5 no.s is 1,2,3,4,5

so average are as

( 1+2+3+4+5)/5=20

if multiplied by 2

then it would b

(1+2+3+4+5)*2/5=20

average is 10

Answer 2

If each number is multiplied by a same number, average will also be multiplied by the same number. therefore answer should be 2 * 20 or 40.

We can prove it mathematically too. .For the proof of the , follow the solution given below. We know that the average of n quantities is $\boxed{\dfrac{\textbf{sum of n quantities}}{\textbf{n}}}$

Given,Average of five numbers = 20  

⇒ $\dfrac{\text{sum of 5 numbers}}{5}=20$

⇒ sum of 5 numbers = 20 x 5

⇒ sum of 5 numbers = 100

Now, Let the numbers are x₁ , x₂ , x₃ , x₄ , x₅ .

So,   x₁ + x₂ + x₃ + x₄ + x₅ = 100       ...( i )

According to the question each number is multiplied by 2.

Now, numbers are 2x₁ , 2x₂ , 2x₃ ,2 x₄ , 2x₅

Their sum = 2x₁ + 2x₂ + 2x₃ + 2x₄ + 2x₅

Number of terms is still same i.e. 5.

∴ New average = $\dfrac{2x₁ + 2x₂ + 2x₃ + 2x₄ + 2x₅}{5}$

⇒$\dfrac{2(x₁ + x₂ + x₃ + x₄ + x₅)}{5}$

Substituting the value of x₁ + x₂ + x₃ + x₄ + x₅ from ( i )

⇒ $\dfrac{2(100)}{5}$

⇒ 2 x 20

⇒ 40

Therefore, new average is 40.