averaging a set of numbers
Message posted by Carol Albertini (via 64.12.105.24) on September 9, 2001 at 9:44 AM (ET)

In our class we had to average mileage per gallon on a set of numbers. Our professor wanted us to answer when it would be appropriate to use total miles divided by total gallons and when we
should use the average of the mpg for each tank. The difference in the calculation is .02 and it seemed insignificant to me. Any ideas?

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Re: averaging a set of numbers
Message posted by Tomi (via 154.32.142.99) on September 9, 2001 at 10:55 AM (ET)

Scenario 1: One car, many measurements.
In this scenario you have measured the fuel consumed and the distance travelled by one car over a period of time. To get an overall measure of miles per gallon, divide the total number of miles by the total number of gallons.

Scenario 2: Many cars, one measurement for each car.
In this scenario you have measured the fuel consumed and distance travelled by a number of cars. For each car you then calculate the mileage per gallon, getting a range of values. This is because you have many different cars, all with different engine sizes, efficiencies etc. To get an idea of the average mileage per gallon for your cars as a group, you then find the mean of these mileages per gallon.

If the number of gallons consumed by each car is roughly the same, then the result to this method will be very similar to that of Scenario 1.

Of course, there is yet a third way!

Scenario 3: Many cars, many measurements for each car.
In this scenario you find the mpg for each car by using (total miles)/(total gallons) as in Scenario 1 and then find the mean of the results for all cars.