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: 

Short-cut method

Answer 1

Short-cut method 

Marks	No. of boys (fi)	Mid-value  xi	A = 65 di = xi – A	fidi
30 – 40	10	35	–30	–300
40 – 50	12	45	–20	–240
50 – 60	14	55	–10	–140
60 – 70	12	A = 65	0	0
70 – 80	9	75	10	90
80 – 90	7	85	20	140
90 – 100	6	95	30	180
Total	70			–270

`barx = A + (sumf_i d_i)/(sumf_i)`

= `65 + ((-270)/70)`

= 65 – 3.86

= 61.14