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

Question 12 Mean Median And Mode Of Ungrouped Data Exercise 18B

Find the missing frequencies in the following frequency distribution whose mean is 50.

x f
10 17
30 f1
50 32
70 f2
90 19
Total 120

x f xifi
10 17 170
30 f1 30f1
50 32 1600
70 f2 70f2
90 19 1710
Total 120 = Σ fi =68 + f1 + f2 Σ fi xi = 3480 + 30f1 + 70f2

We know that

Σ fi =68 + f1 + f2

It can be written as

120 = 68 + f1 + f2

So we get

f1 + f2 = 52

f2 = 52 - f1 ……. (1)

It is given that

Mean = 50

We know that

Mean = Σ fi xi/ Σ fi

So we get

(3480 + 30f1 + 70f2)/ 120 = 50

Substituting equation (1)

3480 + 30f1 + 70(52 - f1) / 120 = 50

On further calculation

(3480 + 30f1 + 3640 – 70f1)/ 120 = 50

So we get

(7120 - 40f1)/ 120 = 50

It can be written as

6000 = 7120 - 40f1

By subtraction

40f1 = 1120

By division

f1 = 28

By substituting it in equation (1)

f2 = 52 – 28 = 24

Therefore, the missing frequencies are 28 and 24.

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