Question

Calculate the mean of the following data using step-deviation method:

Class Interval	40 – 42	43 – 45	46 – 48	49 – 51	52 –54
Frequency	7	10	15	9	8

Answer 1

There are no continuous class intervals.

The distance between two class intervals is one.

So, we have to add `1/2` i.e., 0.5 to the upper-class limit and subtract 0.5 from the lower-class limit of each interval.

Class Interval	Corrected Class Interval	Frequency `(f_i)`	Class mark `x_i`	`d_i = x_i - 47`	`u_i = d_i/h`	`f_i u_i`
40 – 42	39.5 – 42.5	7	41	– 6	– 2	– 14
43 – 45	42.5 – 45.5	10	44	– 3	– 1	– 10
46 – 48	45.5 –48.5	15	47 = A	0	0	0
49 –51	48.5 – 51.5	9	50	3	1	9
52 –54	51.5 – 54.5	8	53	6	2	16
		`sumf_i` = 49				`sumf_i u_i` = 1

Mean, `barX = A + ((sumf_i u_i)/(sumf_i)) xx h`

Here, A = 47, `sumf_i u_i` = 1, `sumf_i` = 49, h = 3

`barx = 47 + (1/49) xx 3`

= `47 + (3/49)`

= 47 + 0.061 = 47.061

≈ 47.1

Therefore, 47.1 is the mean.