Bad Statistics?
21st September 2006
Here is an excerpt from an Associated Press report that was published in my local newspaper this past Sunday (17 Sept. 2006). Some of the information presented in it raises some questions in my mind. I’ve outlined the key statistics in red.
So from the article here’s a summary of the statistics:
In 2004, the percentage of certain borrowers that “paid a higher-than-typical interest rate on their home mortgages” are:
- 32.4% for blacks
- 20.3% for Hispanics
- 8.7% for whites
- 11.5% (all borrowers)
I’m wondering how such a small percentage of all classes are paying “higher-than-typical” rates. Doesn’t logic tell us that exactly 50% of all borrowers will pay a higher-than-typical rate and the other 50% will pay a lower-than-typical rate? Certainly this would be true if the definition of “typical” in this case was “average” or “mean.” So perhaps, “typical” indicates a range of interest rates. Then, the 11.5% indicates the percentage of all borrowers that had interest rates above that range. But if that is the case, it would be very helpful to know the size of that range. Any thoughts?
November 10th, 2006 at 6:58 pm
My first thought is that the median doesn’t have to be equal to the mean. There will be 50% of borrowers equal to or above the median, but if the numbers are skewed (which makes sense for interest rates), the mean could be significantly higher than the median. Also, there seems to be a standard sort of interest rate at any given time, and a lot of people get exactly that rate on a home loan, so you could conceivably have 60% of all home buyers getting exactly the typical home interest rate, with only 40% split between above that and below that.