The mean of the following distribution is 50.

x f

10 17

30 5a+3

50 32

70 7a-11

90 19

Find the value of a and hence the frequencies of 30 and 70.

Question

The mean of the following distribution is 50 Find the value of a and hence the frequencies of 30 and 70

Accepted Answer

It is given that Mean 50 We know that Mean fi xi fi So we get 2800 640a 60 12a 50 On further calculation 2800 640a 3000 600a So we get 40a 200 By division a 5 We know that Frequency of 30 5a 3 By substituting the values Frequency of 30 5 5 3 So we get Frequency of 30 28 We know that Frequency of 70 7a 11 By substituting the values Frequency of 70 7 5 11 So we get Frequency of 70 24 Therefore the value of a is 5 and the frequencies of 30 and 70 is 28 and 24

x	f	xifi
10	17	170
30	5a+3	150a + 90
50	32	1600
70	7a-11	490a - 770
90	19	171
Total	Σ fi = 60 + 12a	Σ fi xi = 2800 + 640a

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