What's the average of 5 MPG and 10 MPG?
The math isn't quite obvious to me, but if you go out camping and get 5 MPG on the way to the campground and turn around and get 10 MGP on the way back, your average MPG won't be 7.5 as you would expe...
Forum Discussion
hotbyte wrote:
How do you get 2/.3 = 10?
And, this is the average (harmonic mean) mpg of 5mpg and 10mpg. What you are stating with the need for the total miles and gallons is the cumulative rate for the vehicle over 2 (or more) trips.toedtoes wrote:hotbyte wrote:dave54 wrote:
http://www.cut-the-knot.org/arithmetic/HarmonicMean.shtml
In math geek talk average and mean are not the same thing. There are different kinds of means, one of which is the arithmetic mean, commonly called average. This problem uses the harmonic mean.
This is the answer. Harmonic mean is used to average rates and MPG is a rate (miles PER gallon). So the average of 5mpg and 10mpg is 2 / ( 1/5 + 1/10 ).
X = 2 / (1/5 + 1/10)
X = 2 / (.2 + .1)
X = 2 / (.3)
X = 10
?????
That is NOT the answer. The answer is that you cannot determine the mean/average/harmonic/arithmetic/or otherwise by only looking at the mpg of two different trips. You have to go to the original data (miles driven and gallons used) to get the answer.
Oops - sorry about my math error - not sure how I did that (can I blame my smart phone? :))
But again the the logic of using anything but the original data is faulty. If the gallons used is the same for both trips then the "harmonic mean" of the two MPGs is not what the combined MPG actually is (in that case the arithmetic mean is correct).
So, if you are trying to determine the MPG for an entire trip (as the OP was addressing), then you HAVE to go back to the original data.
