Question

From the data given below state which group is more variable, A or B?

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Group A	9	17	32	33	40	10	9
Group B	10	20	30	25	43	15	7

Answer 1

Firstly, the standard deviation of group A is calculated as follows.

Marks	Group A fi	Mid-point xi	`y_i = (X_i - 45)/10`	yi2	fiyi	fiyi2
10-20	9	15	–3	9	–27	81
20-30	17	25	–2	4	–34	68
30-40	32	35	–1	1	–32	32
40-50	33	45	0	0	0	0
50-60	40	55	1	1	40	40
60-70	10	65	2	4	20	40
70-80	9	75	3	9	27	81
	150				–6	342

Here, h = 10, N = 150, A = 45

The standard deviation of group B is calculated as follows.

Marks	Group B fi	Mid-point xi	`y_i = (X_i - 45)/10`	yi2	fiyi	fiyi2
10-20	10	15	–3	9	–30	90
20-30	20	25	–2	4	–40	80
30-40	30	35	–1	1	–30	30
40-50	25	45	0	0	0	0
50-60	43	55	1	1	43	43
60-70	15	65	2	4	30	60
70-80	7	75	3	9	21	63
	150				–6	366

Since the mean of both the groups is same, the group with greater standard deviation will be more variable.

Thus, group B has more variability in the marks.