Question

The following table shows the marks scored by 80 students in an examination:

Marks	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40
No. of students	3	10	25	49	65	73	78	80

Answer 1

Let us choose a = 17.5, h = 5, then `d_i = x_i – 17.5 and u_i = (x_i− 17.5)/5`

Using step-deviation method, the given data is shown as follows:

Marks	Number of students (cf)	Frequency `(f_i)`	Class mark `(x_i)`	`d_i = x_i` – 17.5	`u_i = (x_i−17.5)/ 5`	`(f_i u_i)`
0 – 5	3	3	2.5	-15	-3	-9
5 – 10	10	7	7.5	-10	-2	-14
10 – 15	25	15	12.5	-5	-1	-15
15 – 20	49	24	17.5	0	0	0
20 – 25	65	16	22.5	5	1	16
25 – 30	73	8	27.5	10	2	16
30 – 35	78	5	32.5	15	3	15
35 – 40	80	2	37.5	20	4	8
Total		`Ʃ f_i = 80`				`Ʃ f_i u_i = 17`

The mean of the given data is given by,

x = a+ `((Ʃ_i  f_i u_i )/(Ʃ_i f_i)) xx h`

   = `17.5 + (17/80) xx 5`

  = 17.5 + 1.06
  = 18.56
Thus, the mean marks correct to 2 decimal places is 18.56.