The following table shows the marks scored by 140 students in an examination of a certain paper: Marks: 0-10 10-20 20-30 30-40 40-50 Number of students: 20 24 40 36 20 Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Question

Philoid · Accepted Answer

From Direct method:

Class interval	Mid value (x_i)	f_i	f_ix_i
0-10	5	20	100
10-20	15	24	360
20-30	25	40	1000
30-40	35	36	1260
40-50	45	20	900
		N = 140	∑f_ix_i = 3620

Mean =

= = 25.857

Assumed mean method: let assumed mean (A) = 25

Mean = A +

Class interval	Mid value (x_i)	u_i = x_i – A	f_i	f_iu_i
0-10	5	-20	20	-400
10-20	15	-10	24	-240
20-30	25	0	40	0
30-40	35	10	36	360
40-50	45	20	20	400
			N = 140	∑f_iu_i = 120

Mean = A +

= 25 + = 25 + 0.857

= 25.857

Step deviation method: Let the assumed mean (A) = 25

Class interval	Mid value (x_i)	d_i = x_i – A = x_i - 25	u_i =	Frequency (f_i)	f_iu_i
0-10	5	-20	-2	20	-40
10-20	15	-10	-1	24	-24
20-30	25	0	0	40	0
30-40	35	10	1	36	36
40-50	45	20	2	20	40
				N = 140	∑f_iu_i = 12

Mean = A + * h

= 25 + * 10

= 25 + 0.857 = 25.857

The following table shows the marks scored by 140 students in an examination of a certain paper:Marks:0-1010-2020-3030-4040-50Number of students:2024403620Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

The following table shows the marks scored by 140 students in an examination of a certain paper:

Marks:

0-10

10-20

20-30

30-40

40-50

Number of students:

20

24

40

36

20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.