Question

Find the mean by step deviation method. 

Class	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	5	6	8	12	6	3

Answer 1

1. Formula

The formula for finding the mean using the step-deviation method is:

Mean `(barx) = A + ((sumf_iu_i)/(sumf_i)) xx h`

Where:

A = Assumed mean (middle value from class marks x_i)

h = Class width (upper limit – lower limit = 15 – 10 = 5)

`u_i = (x_i - A)/h`

x_i = Class mark (midpoint of each class) = `("Lower limit" + "Upper limit")/2`

2. Calculation table

The assumed mean A = 22.5 and class width h = 5:

Class	Frequency (fi)	Class Mark (xi)	`bb(u_i = (x_i - 22.5)/5)`	fiui
10 – 15	5	12.5	–2	–10
15 – 20	6	17.5	–1	–6
20 – 25	8	22.5 (A)	0	0
25 – 30	12	27.5	1	12
30 – 35	6	32.5	2	12
35 – 40	3	37.5	3	9
Total	Σfi = 40			Σfiui = 40

 

3. Substitute values into the formula

Substituting the sums into the step deviation equation:

`barx = 22.5 + (17/40) xx 5`

`barx = 22.5 + 17/8`

`barx` = 22.5 + 2.125

`barx` = 24.625