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	5

Answer 1

1. Identify the formula

The formula for the mean `(barx)` using the step deviation method is:

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

Where:

A: Assumed mean a value from the middle of the class marks.

h: Class size width of the interval, e.g., 15 – 10 = 5.

f_i: Frequency of each class.

x_i: Class mark (midpoint) of each class `(("Lower Limit" + "Upper Limit")/2)`.

u_i: Step deviation, calculated as `u_i = (x_i -A)/h`.

2. Calculation table

We will pick A = 22.5 as our assumed mean.

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	5	37.5	3	15
Total	Σfi = 42			Σfiui = 23

3. Final calculation

Now, substitute the values into the formula:

`barx = 22.5 + (23/42) xx 5`

`barx = 22.5 + 115/42`

`barx ≈ 22.5 + 2.738`

`barx ≈ 25.238`

The mean of the given data is approximately 25.24.