1.

The mean of 15 numbers is 27. If each number is multiplied by 4, what will be the mean of the new numbers?

Answer»

Consider x1, x2, ……. x15 as the given numbers

So we get

Mean = (x1 + x2 + ……. + x15)/15

It is given that mean = 27

(x1 + x2 + ……. + x15)/15 = 27

By cross multiplication

x1 + x2 + ……. + x15 = 405 …… (1)

Take (x1 × 4), (x2 × 4), ……… (x15 × 4) as new numbers

So the mean of new numbers = [(x1 × 4) + (x2 × 4) + ……… + (x15 × 4)]/15

From equation (1) we get

[(x1 × 4) + (x2 × 4) + ……… + (x15 × 4)]/15 = (405 × 4)/ 15

On further calculation

Mean of new numbers = 1620/15 = 108

Therefore, the mean of new numbers is 108.


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