[If you are interested in trading in a car in the Cash for Clunkers program, be sure to check the size and value of your gas savings at this post. The gas savings can be worth as much as the voucher. DOT has released more detailed numbers about cars sold and bought, and this August 5 post analyzes the benefits so far of Cash for Clunkers.]

There is a story that has received a lot of attention in the last 2 days stating that early trade ins in the Cash for Clunkers program have reaped a 69% improvement over the original "clunker."

Here's the press release: http://www.webwire.com/ViewPressRel.asp?aId=100063

It's an encouraging number if true. (Of course, in terms of reduction in gas consumption, the percentage translates to 40% as spelled out here.)

However, until the organization produces more concrete numbers, we have to worry that they took straight averages of MPG across vehicles without actually calculating the harmonic mean, i.e., converting all cars to GPM before MPG, as done in the CAFE calculations.

Why does it matter? Let's create a simple scenario:

• The average clunker trade in gets 16mpg

• The average new vehicle gets 27mpg

11 divided by 16 represents a 69% increase over the original MPG. Let's assume two 16 MPG cars were turned in, one for a 20 MPG car and the other for a 34 MPG car. The average MPG appears to be 27 MPG. However, the actual MPG of the two new cars is 2/(1/20 + 1/34), or 25 MPG. A good improvement, but not a 69% improvement; it's a 56% improvement.

The harmonic mean keeps very efficient cars from incorrectly inflating the overall MPG.