# RS Aggarwal Solutions Class 9 Mathematics Solutions for Mean Median And Mode Of Ungrouped Data Exercise 18A in Chapter 18 - Mean Median And Mode Of Ungrouped Data

Question 9 Mean Median And Mode Of Ungrouped Data Exercise 18A

The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers, what will be the new mean?

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

So we get

Mean = (x1 + x2 + ……. + x20)/20

It is given that mean = 43

(x1 + x2 + ……. + x20)/20 = 43

By cross multiplication

x1 + x2 + ……. + x20 = 860 …… (1)

Take (x1 – 6), (x2 – 6) …… (x20 – 6) as the new numbers

So the mean of new numbers = [(x1 – 6) + (x2 – 6) + …… + (x20 – 6)]/20

From equation (1) we get

[(x1 – 6) + (x2 – 6) + …… + (x20 – 6)]/20 = (860 – 120)/20

On further calculation

[(x1 – 6) + (x2 – 6) + …… + (x20 – 6)]/20 = 740/20

By division

Mean of new numbers = 37

Therefore, the new mean of numbers is 37.

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