Question

Calculation (i) Arithmetic Mean (ii) Standard Deviation and (iii) Co-efficient of variation for the following frequency distribution.

Class Interval	Frequency
30 – 35 35 – 40 40 – 45 45 – 50 50 – 55	5 10 16 15 4
Total	50

Answer 1

Table of calculation
Class Interval (Rs)	Frequency f	Mid-point X	fX	Deviation	Square of Deviation D2	f.D2
30 – 35	5	32.5	162.5	–10.268	105.431824	527.15912
35 – 40	10	37.5	375	–5.268	27.751824	277.51824
40 – 45	16	42.4	678.4	–0.368	0.135424	2.166784
45 – 50	15	47.5	712.5	4.732	22.391824	335.87736
50 – 55	4	52.5	210	9.732	94.711824	378.847296
	= 50		2138.4			=1521.5688

Sum of the frequencies = N = = 50

(i) Mean = = = 42.8

(ii) = = = 5.52

(iii) C.V= = = 12.89