Q52. Explain the use of Coefficient of Variation with examples.
Coefficient of variation is the ratio of standard deviation to the mean. The higher the CV, the more is the spread of the data around its mean and the team or process is very unstable or ununiformed. In simple, it is % variation in mean, where SD is total variation in mean. It is a measure of relative variability.
This is used to compare variations of two or more data sets.
For Eg. If I have to compare results of two groups lets say Group A & Group B. Group A has CV of 25% and Group B has CV of 18%. This says that the Group A has more variability to its mean.
Formula for CV = SD / mean
It can be expressed as in percentage %. Hence the formula for CV can be multiplied by 100.
Benefits of CV –
1. Measure of Precision – It is used to describe the level of variations existing within the population independently from the absolute values of the individual observations. If the population is same, where you have to find out the variation, then use Standard deviation. If the population is different, use this CV to estimate the spread or variability from its relative mean.
Eg. If Male and female elephant group is compared, then use SD to find out the variation.
If you have to compare the male elephant population with male mice population, then use CV.
In simple, when the two groups differ significantly, use CV as a measure. It is to assess the precision of the measurement technique.
2. Measure of Repeatability - CV is used to measure the repeatability within the group and not the validity / reproducibility. It is used in a way to tell you the degree of association but not agreement. Measuring repeatability with out validity is a useful analysis. When assessing the measurement error, CV value depends on both the variability between sampling units and variability between repeated readings from the same user. If we have to select the variable group of sampling units, then the repeatability CV would be higher than taking up for a homogenous group. The aim is to be maximize the repeatability within the given situation.
Eg. Used by Microbiologists and pharmacist to evaluate the intra assay and inter assay CV, in order to bring down the CV value to make it acceptable.
3. Consistency of data – CV is used to understand and confirm the consistency of data. Consistency means uniformity in the values of the data set. How consistent the values are from the mean of the data set is measured. As small as the CV means the data is uniform or consistent.
Eg. If the temperature of an adult is to be compared to the same of a newborn, certain values are recorded In the real time for some time. Hence CV for adult is 10% and CV for newborn is of 2%. As for Newborn the CV is smaller, the variation in the data is very minimal. Means the data for Newborn is consistent than adult.
4. Indicator for Risk Assessment – It is a better indicator for all levels of risk assessment. In any type of situation, if we were to assess the risk, this would be the right tool.
Eg. If Bank A gives a rate of interest at 20% and Bank B gives u at 10%, with a standard deviation of 10% and 5% respectively. Which bank is better to take a loan?
As Bank B has SD of 5%, the Rate of interest is minimal for a longer run to balance his needs by the customer. Hence customer would prefer Bank B.
5. Decision making: If the team has to downsize due to high cost, the decision is to eliminate some of the team members. CV Is a useful tool where it tells us in which team ,there is more of variability, which team receives higher cost , etc to make strategic decisions.
Eg. Organization has two functions – coding and billing with 40 and 65 employees in it. They earn around $450 and $350 respectively with SD as 7 and 9.
Q – A) which section has a higher salary package? Which function has highest variability?
Answer –
a) Salary for Coding = 40 *450 = 18000
Salary for billing = 65 * 350 = 22750
So, Salary for billing is higher.
CV for Coding =( 7/450) *100 = 1.6%
CV for billing =( 9/350) *100 = 2.6%
Billing is more of variability since it has more CV.
The Zero disadvantage:
CV is useful only for the calculations, when the mean of sample population is not zero.
Lets assume, if the sample mean is equal to zero, then the denominator would become zero. Hence the CV gets nullified.
Yes. CV is useful if all the data points or atmost of the data points share the same value as of plus or minus sign.
Conclusion:
CV has its own use and limitations. Hence it should used to carefully in
1. Estimating the variation 2 different populations
2. Estimating the 2 set of categories variations.
3. Risk assessment indicator
4. Decision making
Thanks
Kavitha