Statistics - Co-efficient of Variation

Statistics – Co-efficient of Variation

Coefficient of Variation

Normal variation is an absolute measure of dispersion. When comparability must be made between two collection then the relative measure of dispersion, generally known as coeff.of variation is used.

Coefficient of Variation, CV is outlined and given by the next perform:

Formulation

CV=σX×100CV=σX×100

The place −

  • CVCV = Coefficient of Variation.
  • σσ = customary deviation.
  • XX = imply.

Instance

Downside Assertion:

From the next knowledge. Determine the dangerous mission, is extra dangerous:

12 months 1 2 3 4 5
Undertaking X (Money revenue in Rs. lakh) 10 15 25 30 55
Undertaking Y (Money revenue in Rs. lakh) 5 20 40 40 30

Resolution:

As a way to determine the dangerous mission, we’ve got to determine which of those tasks is much less constant in yielding earnings. Therefore we work out the coefficient of variation.

Undertaking X Undertaking y
XX XiX¯Xi−X¯
xx
x2x2 YY YiY¯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

Undertaking X

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

Undertaking Y

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

Since coeff.of variation is larger for mission X than for mission Y, therefore regardless of the typical earnings being identical, mission X is extra dangerous.