1.

The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

Answer»

Consider x1, x2, …….. x24 as the given numbers

So we get

Mean = (x1 + x2, …….. + x24)/24

It is given that mean = 35

(x1 + x2, …….. + x24)/24 = 35

By cross multiplication

x1 + x2, …….. + x24 = 840 ……. (1)

Take (x1 + 3), (x2 + 3), ……… (x24 + 3) as new numbers

So the mean of new numbers = [(x1 + 3) + (x2 + 3) + ……… + (x24 + 3)]/24

From equation (1) we get

[(x1 + 3) + (x2 + 3) + ……… + (x24 + 3)]/24 = (840 + 72)/24

On further calculation

[(x1 + 3) + (x2 + 3) + ……… + (x24 + 3)]/24 = 912/24

By division

Mean of new numbers = 38

Therefore, the mean of the new numbers is 38.


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