Question

when would you use the coefficient variation in ecobomics?

Answer 1

Coefficient Variation

Definition: The coefficient of variation also known as relative standard deviation is a statistical measure of the dispersion of data points around the mean.

Formula: CV = (standard deviation / mean) * 100

Usage -

1. The metric is commonly used to compare the data dispersion between distinct series of data.

2. It is a simple and quick tool to compare different data series.

3. This metric is useful for comparing variables that have different standard deviations and different means.

4. In the context of finance, we can think of the CV as a measure of relative dispersion that can be used to compare the risks of assets that have different mean (expected) returns.

Example (Principles of Managerial Finance, Lawrence J. Gitman) -

Let’s assume we have two corn hybrids that average 150 bushels an acre, and hybrid A’s yield has a standard deviation of 10 bushels per acre, while hybrid B’s yield has a standard deviation of 50 bushels an acre. If we are about to plant one of these hybrids, we know that hybrid A is going to provide us more certainty about our expected yields in the fall. The empirical rule tells us that about 95% of the time if we plant hybrid A, our yields will be between 130 and 170 bu/acre. If we plant hybrid B, 95% of the time yields will be between 50 and 250 bu/acre.

So, with two hybrids with the same average yield, we know that the one with the lower standard deviation will perform more consistently. But what if they both have different yields and different standard deviations?

Hybrid A: mean 185 bu;/acre std dev: 5 bu/acre

Hybrid B: mean: 200 bu/acre std dev: 30 bu/acre

Choosing the most reliably yielding hybrid in this case is not quite so easy. But the CV helps us make the comparison:

Hybrid A: CV = (5/185) *100 = 2.7%

Hybrid B: CV = (30/200)*100 = 15%

We can see by the CV that hybrid A, even though it yields on average less than hybrid B, will deliver more consistent results.