Question

Using step-deviation method, calculate the mean marks of the following distribution.

C.I.	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80	80 – 85	85 – 90
Frequency	5	20	10	10	9	6	12	8

Answer 1

Let the assumed mean A = 72.5 

C.I.	fi	Mid-value (xi)	A = 72.5 `bb(t = (x - A)/i)`	fiti
50 – 55	5	52.5	–4	–20
55 – 60	20	57.5	–3	–60
60 – 65	10	62.5	–2	–20
65 – 70	10	67.5	–1	–10
70 – 75	9	72.5	0	0
75 – 80	6	77.5	1	6
80 – 85	12	82.5	2	24
85 – 90	8	87.5	3	24
Total	80			–56

Mean = `A + (f_it_i)/n xx i`

= `72.5 + (-56/80) xx 5`

= 72.5 – 0.7 × 5

= 72.5 – 3.5

= 69