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

Question

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

Accepted Answer

We know that 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 fi xi fi So we get 3480 30f1 70f2 120 50 Substituting equation 1 3480 30f1 7052 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

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

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