Wednesday, May 24, 2006

An Appropriate Median

In real life I seldom find use for an average other than the arithmetic mean (where you sum all the values and then divide by the number of values). Statistics includes two others types of average. The median is the central value if the values were sorted in increasing order. The mode is the most commonly occuring value.

A co-worker at LCC pointed out yesterday an application of averages in an LCC announcement. A mean is used (of $141) when a median would be more appropriate.

The community college has its own health clinic. The announcement was: indicates that the average cost of a medical provider visit in Eugene is $141. The Lane Health Clinic currently sees 100 employees per month: That's $14,100 per month not billed to insurance. This translates to a $500,000 to $700,000 decrease in insurance renewal rates secondary to decreased insurance utilization.
(I'm not sure what math was done to support the final statement, which claims insurance rates are greater than insurance use by at least 300%. Were that true, it would seem time to find a new insurance company.)

My co-worker's point about averages was that the $141 is an arithmetic mean of all medical visits, which include many procedures beyond what the college health clinic is able to do. This is one example of when it would be better to use the median instead of the mean. Since less expensive procedures happen much more often in doctor office visits, if we were to list the costs of all the city's medical visits in increasing order and pick the middle one then we would find a number more representative of the average procedure of the college health clinic.

Maybe this only seems worthy of comment because I am a mathematician. But it fascinated me that I so seldom see a situation where using the median is more appropriate than using the mean, and here one appeared within the college itself!