Question

Find the mean of the following distribution by step deviation method:

Class interval	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	10	6	8	12	5	9

Answer 1

C.I.	`f`	'X' mid values	`mu = (x - "A")/"h"`	`f.mu.`
20 - 30	10	25	-3	-30
30 - 40	6	35	-2	-12
40 - 50	8	45	-1	-8
50 - 60	12	55 = A	0	0
60 - 70	5	65	1	5
70 - 80	9	75	2	18
	`sumf = 50`			`sumfmu = -27`

Here,
A = Assumed mean = 55
h = 10
∴ Mean `bar"X" = "A" + (sumfmu)/(sumf) xx "h"`
= 55 + `((-27))/(50) xx 10`
= 55 - 5·4
= 49·6.