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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
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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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