1.

The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers.

Answer»

Consider x1, x2, ……. x20 as the given numbers

So we get

Mean = (x1 + x2 + ……. + x20)/20

It is given that mean = 18

(x1 + x2, ……. + x20)/20 = 18

By cross multiplication

x1 + x2 + ……. + x20 = 360 …… (1)

Take (x1 + 3), (x2 + 3), ……… (x10 + 3) as first ten new numbers

So the mean of new set of 20 numbers = [(x1 + 3) + (x2 + 3) + ……… + (x10 + 3) + x11 + …….. + x20]/ 20

We get

Mean of new set of 20 numbers = [(x1 + x2 + ……. + x20) + 3 × 10]/ 20

From equation (1) we get

Mean of new set of 20 numbers = (360 + 30)/ 20 = 19.5

Therefore, the mean of new set of 20 numbers is 19.5.


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