Question

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.

Answer 1

The formula of the mean `(barx)` is:

`barx = (sum_(i = 1)^n  f_ix_i)/(sum_(i = 1)^n f_i)`

So, the value of a wall be calculated as follows:

`50 = (17 xx 10 + (5a + 3) xx 30 + 32 xx 50 + (7a - 11) xx 70 + 19 xx 90)/(17 + 5a + 3 + 32 + 7a - 11 + 19)`

`50 = (170 + 150a + 90 + 1600 + 490a - 770 + 1710)/(12a + 60)`

`50 = (3570 - 770 + 640a)/(12a + 60)`

2800 + 640a = 600a + 3000

40a = 200

a = 5

So, frequency of 30 will be = 5a + 3 = 5 × 5 + 3 = 25 + 3 = 28

Similarly, frequency of 70 will be = 7a – 11 = 7 × 5 – 11 = 35 – 11 = 24

Therefore, the frequency of 30 and 70 are 28 and 24 respectively.