Latoay,

I think you are probably correct but it's sample variance not simple variance. It is however hard to know exactly what is going on in your teacher's mind. When you are taking measurements of some sort there may be different sources of variation that are measured by different variance measurements.

Suppose you are a car maker, you have just produced a new model and you want to measure the gas mileage. You take two of the new cars and drive them the same route at the same speed and measure the gas mileage. Then you do it again with the same cars but a different route. Repeat a few more times over different routes and then from all the data calculate the mean gas mileage.

There are two sources of variation here, one because the routes are different each time and the other because no two cars are identical:

1. If you look at the data for each car separately you can calculate each cars variance that comes from the different routes. Statisticians call this the variance within the treatment.
2. You can also look at each route separately, calculate the difference in gas mileage between the two cars for each route and then calculate the variance for these differences. Statisticians call this the variance between treatments.

I hope this helps,
Penny