Now think of a running shoe company.

The running shoe company has two models, model 1, and model 2.

It makes forecasts for model 1 and model 2 by thinking about the mean or

the expected amount of shoes that they're going to sell.

It is common in operations and statistics to use the Greek symbol mu to capture

this, and the standard deviation of that demand, which we going to call sigma.

[SOUND] Now we might think about sigma as

the amount of uncertainty that the firm faces.

However, sigma alone, the standard deviation alone, is not a good proxy for

the amount of variability or uncertainty in demand.

A thousand running shoes standard deviation, is that a big number or

a small number?

That really depends on the mu, on the mean.

If I'm having 1,000 standard deviation for an expected demand of 2,000,

we would call this probably a lot of statistical variation.

However, if it's 1,000 standard deviation for

a million shoes, that would be relatively little.

With this in mind, we define the coefficient of variation, also CV,

coefficient of variation as a ratio between the standard deviation and

the mean.

Now consider a competitor of our running shoe business that has somehow

managed to combine shoes 1 and 2 into one model.

Think of this as, again, shoes for men and shoes for

female runners, whereas this company has just one common shoe for everybody.

Let's assume for

the sake of argument that the demand for the female running shoes and

the demand for the male running shoes are independent of each other.

Moreover, let's assume that the market sizes are roughly similar and

the market uncertainties are also roughly similar.

In other words, the mu1 is equal to the mu2,

and the sigma 1 is equal to the sigma 2.