StATS: Fractions are funny (December 13, 2005)

On my web page about odds ratios, I point out the fractions are funny and cite some well known examples of how fractions behave in a counter intuitive fashion. One of the examples I cite is a Car Talk Puzzler problem about a 100 pound sack of potatoes.  I cited the puzzler book that Tom and Ray Magliozzi had published:

but you can also find this question and answer on the web at

Just recently, the Car Talk guys published another examples of how fractions are funny. It is a simpler example, but it is still interesting. One year National Public Radio decides to give Tom a 10% raise and Ray a 10% pay cut (for PPP -- Poor Puzzler Performance). The following year, Tom gets the 10% pay cut and Ray gets a 10% raise. They ask who ends up with more money.

The answer is surprising, not in who gets more money but the fact that both of them are making less money after two years, even though they seemed to get offsetting pay raises and pay cuts. The full details of this puzzler question and answer are at

The fact that a 10% raise and 10% pay cut do not offset one another may not be immediately apparent, but when you consider a more extreme case, a 100% pay raise and a 100% pay cut, it becomes more apparent.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Measuring benefit and risk.