Question

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.

Answer 1

Direct method

Class interval	Mid value(x1)	Frequency(f1)	f1x1
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	3620

Mean `=(sumf_1"u"_1)/N`

`=3620/140=25.857`

 

Assume mean method : Let the assumed mean = 25

Class interval	Mid value(x1)	u1 = x1 - 25	f1	f1u1
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	120

Mean `=A+(sumf_1"u"_1)/N`

`=25+120/140`

= 25 + 0.857

= 25.857

 

Step deviation method

Let the assumed mean A = 25

Class interval	Mid value(x1)	d1 = x1 - 25	`"u"_1=(x_1-25)/10`	f1	f1u1
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	12

Mean `=A+hxx(sumf_1"u"_1)/N`

`=25+10xx12/140`

`=25+120/140`

= 25 + 0.857

= 25.857