Question

Given that the mean of the following frequency distribution is 30, find the missing frequency ‘f’.

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	4	6	10	f	6	4

Answer 1

Class interval	Frequency (f)	x	d = x - A	t = `"d"/"i"`	ft
0 - 10	4	5	- 30	- 3	- 12
10 - 20	6	15	- 20	- 2	- 12
20 - 30	10	25	- 10	- 1	- 10
30 - 40	f	35 = A	0	0	0
40 - 50	6	45	10	1	6
50 - 60	4	55	20	2	8

Step deviation method,

∑f = 30 + f, A = 35, Class width (i) = 10

and ∑ft = - 34 + 14 = - 20

∴ Mean = A + `(sum "ft")/(sum "f") xx "i"`

`=> 30 = 35 + (- 20)/(30 + "f") xx 10`

`=> - 5 = (- 200)/(30 + "f")`

`=> 30 + "f" = 200/5`

⇒ 30 + f = 40

⇒ f = 40 - 30

⇒ f = 10