Question

Find the mean by step deviation method:

Class	0 – 20	20 – 40	40 –60	60 – 80	80 – 100	100 – 120
Frequency	20	35	52	44	38	31

Answer 1

Step 1: Prepare the data table

We will identify the class marks (x_i) and calculate the step deviations (u_i).

Class size (h): 20 (Since 20 – 0 = 20)

Assumed Mean (A): Let’s choose the middle class mark, 70.

Class	Frequency (fi)	Class Mark (xi)	`bb(u_i = (x_i - 70)/20)`	fiui
0 – 20	20	10	–3	–60
20 – 40	35	30	–2	–70
40 – 60	52	50	–1	–52
60 – 80	44	70	0	0
80 – 100	38	90	1	38
100 – 120	31	110	2	62
Total	Σfi = 220			Σfiui = –82

Step 2: Calculate the mean

Now, we substitute the values into the formula:

1. Sum of frequencies (Σf_i): 220

2. Sum of f_iu_i: –60 – 70 – 52 + 0 + 38 + 62 = –82

3. Calculation:

`barx = 70 + ((-82)/(220)) xx 20`

`barx = 70 + ((-82)/(11))`

`barx = 70 - 7.4545...`

`barx ≈ 62.55`

The mean of the given data is approximately 62.55.