Using step – deviation method, find mean for the following data. Give your answer to the nearest of a whole number.

Marks	Class Mark (x)	d = x - A	u = d/i	Frequency (f)	fu
20 – 25	22.5	−10	−2	10	−20
25 – 30	27.5	−5	−1	7	−7
30 – 35	A = 32.5	0	0	9	0
35 – 40	37.5	5	1	13	13
40 – 45	42.5	10	2	5	10
45 – 50	47.5	15	3	6	18
Total				Σf = 50	Σfu = 14

Let assumed mean A = 32.5 and class size $i = 5$.

By formula,

Mean = A + $\frac{Σfu}{Σf} \times i$

$$\begin{aligned}= 32.5 + \frac{14}{50} \times 5 \\[1em] = 32.5 + \frac{70}{50} \\[1em] = 32.5 + 1.4 \\[1em] = 33.9 \\[1em] ≈ 34.\end{aligned}$$

Hence, the mean = 34.