Question

Mean of 12 numbers is 20. If each number is multiplied by 6, then the new mean is ………​

Answer 1

Step-by-step explanation:

The mean of 12 numbers is 20.

So if each number is multiplied by 6, the new mean will be 20*6 = 120. Answer.

Answer 2

The new mean is 120

Given :

• Mean of 12 numbers is 20.

• Each number is multiplied by 6

To find :

The new mean

Solution :

Step 1 of 2 :

Calculate sum of new set of numbers

Let the given 12 numbers are a₁ , a₂ , a₃ , a₄ , . . . , a₁₁ , a₁₂

Since mean of 12 numbers is 20

∴ Sum of given 12 numbers

= a₁ + a₂ + a₃ + a₄ + . . . + a₁₁ + a₁₂

= 12 × 20

= 240

Now each number is multiplied by 6

So given 12 numbers becomes 6a₁ , 6a₂ , 6a₃ , 6a₄ , . . . , 6a₁₁ , 6a₁₂

∴ Sum of new set of numbers

= 6a₁ + 6a₂ + 6a₃ + 6a₄ + . . . + 6a₁₁ + 6a₁₂

= 6(a₁ + a₂ + a₃ + a₄ + . . . + a₁₁ + a₁₂)

= 6 × 240

= 1440

Step 2 of 2 :

Calculate the new mean

The new mean

$\displaystyle \sf = \frac{1440}{12}$

$\displaystyle \sf = 120$

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