Question

The following are the marks obtained by 70 boys in a class test:

Marks	No. of boys
30 – 40	10
40 – 50	12
50 – 60	14
60 – 70	12
70 – 80	9
80 – 90	7
90 – 100	6

Calculate the mean by:  

Step-deviation method

Answer 1

Step-deviation method 

Marks	No. of boys (fi)	Mid-value xi	A = 65      `bb(u_i = (x_i - A)/h)`	fiui
30 – 40	10	35	–3	–30
40 – 50	12	45	–2	–24
50 – 60	14	55	–1	–14
60 – 70	12	A = 65	0	0
70 – 80	9	75	1	9
80 – 90	7	85	2	14
90 – 100	6	95	3	18
Total	70			–27

Here A = 65 and h = 10 

`barx = A + h xx (sumf_iu_i)/(sum f_i)`

= `65 +10 xx ((-27)/70)`

= 65 – 3.86

= 61.14