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=ÏƒXÃ—100CV=ÏƒXÃ—100

The place âˆ’

• CVCVÂ = Coefficient of Variation.
• ÏƒÏƒÂ = customary deviation.
• XXÂ = imply.

### Instance

Downside Assertion:

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

 12 months Undertaking X (Money revenue in Rs. lakh) Undertaking Y (Money revenue in Rs. lakh) 1 2 3 4 5 10 15 25 30 55 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 Xiâˆ’XÂ¯Xiâˆ’XÂ¯
xx
x2x2 YY Yiâˆ’YÂ¯Yiâˆ’YÂ¯
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
âˆ‘X=135âˆ‘X=135 âˆ‘x2=1230âˆ‘x2=1230 âˆ‘Y=135âˆ‘Y=135 âˆ‘y2=880âˆ‘y2=880

Undertaking X

HereÂ XÂ¯=âˆ‘XN=âˆ‘1355=27andÂ Ïƒx=âˆ‘X2Nâˆ’âˆ’âˆ’âˆ’âˆšâ‡’Ïƒx=12305âˆ’âˆ’âˆ’âˆ’âˆš=246âˆ’âˆ’âˆ’âˆš=15.68â‡’CVx=ÏƒxXÃ—100=15.6827Ã—100=58.07Right hereÂ XÂ¯=âˆ‘XN=âˆ‘1355=27andÂ Ïƒx=âˆ‘X2Nâ‡’Ïƒx=12305=246=15.68â‡’CVx=ÏƒxXÃ—100=15.6827Ã—100=58.07

Undertaking Y

HereÂ YÂ¯=âˆ‘YN=âˆ‘1355=27andÂ Ïƒy=âˆ‘Y2Nâˆ’âˆ’âˆ’âˆ’âˆšâ‡’Ïƒy=8805âˆ’âˆ’âˆ’âˆš=176âˆ’âˆ’âˆ’âˆš=13.26â‡’CVy=ÏƒyYÃ—100=13.2527Ã—100=49.11Right hereÂ YÂ¯=âˆ‘YN=âˆ‘1355=27andÂ Ïƒy=âˆ‘Y2Nâ‡’Ïƒy=8805=176=13.26â‡’CVy=ÏƒyYÃ—100=13.2527Ã—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.