Coefficient of Variation

Standard variation is an absolute measure of dispersion. When comparison has to be made between two series then the relative measure of dispersion, known as coeff.of variation is used.

Coefficient of Variation, CV is defined and given by the following function:

Formula

CV=σX×100CV=σX×100

Where −

·        CVCV = Coefficient of Variation.

·        σσ = standard deviation.

·        XX = mean.

Example

Problem Statement:

From the following data. Identify the risky project, is more risky:

Year	1	2	3	4	5
Project X (Cash profit in Rs. lakh)	10	15	25	30	55
Project Y (Cash profit in Rs. lakh)	5	20	40	40	30

Solution:

In order to identify the risky project, we have to identify which of these projects is less consistent in yielding profits. Hence we work out the coefficient of variation.

Project X	Project y
XX	Xi−X¯Xi−X¯  xx	x2x2	YY	Yi−Y¯Yi−Y¯  yy	y2y2
10	-17	289	5	-22	484
15	-12	144	20	-7	49
25	-2	4	40	13	169
30	3	9	40	13	169
55	28	784	30	3	9
∑X=135∑X=135		∑x2=1230∑x2=1230	∑Y=135∑Y=135		∑y2=880∑y2=880

Project X

Here X¯=∑XN=∑1355=27and σx=∑X2N−−−−√⇒σx=12305−−−−√=246−−−√=15.68⇒CVx=σxX×100=15.6827×100=58.07Here X¯=∑XN=∑1355=27and σx=∑X2N⇒σx=12305=246=15.68⇒CVx=σxX×100=15.6827×100=58.07

Project Y

Here Y¯=∑YN=∑1355=27and σy=∑Y2N−−−−√⇒σy=8805−−−√=176−−−√=13.26⇒CVy=σyY×100=13.2527×100=49.11Here Y¯=∑YN=∑1355=27and σy=∑Y2N⇒σy=8805=176=13.26⇒CVy=σyY×100=13.2527×100=49.11

Since coeff.of variation is higher for project X than for project Y, hence despite the average profits being same, project X is more risky.