Question

Marks obtained in a test by X standard students of two sections A and B are given below:

Marks	No. of students in Section A	No. of students in Section B
25 – 30 30 – 35 35 – 40 40 – 45 45 – 50	5 10 25 8 2	5 12 20 8 5

Determine: (i) Which section’s performance is better? And (ii) Which section’s performance is more variable?

Answer 1

Table of calculation for section A
Class Interval (Rs)	Frequency f	Mid-point X	fX	Deviation	Square of Deviation D2	f.D2
25 – 30	5	27.5	137.5	– 9.2	84.64	423.2
30 – 35	10	32.5	325	– 4.2	17.64	176.4
35 – 40	25	37.5	937.5	0.8	0.64	16
40 – 45	8	42.5	340	5.8	33.64	269.12
45 – 50	2	47.5	95	10.8	116.64	233.28
	= 50		1835			=1118

Sum of the frequencies = N = = 50

(i) Mean = = = 36.7

(ii) = = = 4.73

(iii) C.V = = = 12.90

Table of calculation for section B
Class Interval (Rs)	Frequency f	Mid-point X	fX	Deviation	Square of Deviation D2	f.D2
25 – 30	5	27.5	137.5	–9.6	92.16	460.8
30 – 35	12	32.5	390	–4.6	21.16	253.92
35 – 40	20	37.5	750	0.4	0.16	3.2
40 – 45	8	42.5	340	5.4	29.16	233.28
45 – 50	5	47.5	237.5	10.4	108.16	540.8
	= 50		= 1855			= 1492

Sum of the frequencies = N = = 50

(i) Mean = = = 37.1

(ii) == = 5.463

(iii) C.V= = = 14.73

The mean marks obtained by the students of section B is greater than that obtained by the students of section A.

Hence, section B’s performance is better.

The coefficient of variation for section B is more than that for section A.

Hence, the performance of section B is more variable.