Statistics Lesson and Warning of the Day – Confusion Between the Median and the Average
April 25, 2014 4 Comments
Yesterday, I attended an interesting seminar called “Transforming Healthcare through Big Data” at the Providence Health Care Research Institute‘s 2014 Research Day. The seminar was delivered by Martin Kohn from Jointly Health, and I enjoyed it overall. However, I noticed a glaring error about basic statistics that needs correction.
Martin wanted to highlight the overconfidence that many doctors have about their abilities, and he quoted Vinod Kohsla, the co-founder of Sun Microsystems, who said, “50% of doctors are below average.” Martin then presented a study showing an absurdly high percentage of doctors who think that they are “above average”. A Twitter conversation between attendees of a TED conference in San Francisco and Vinod himself confirms this quotation.
The statement “50% of doctors are below average” is wrong in general. By definition, 50% of any population is below the median, and the median is only equal to the average if the population is symmetric. (Examples of symmetric probability distributions are the normal distribution and the Student’s t-distribution.) Vinod meant to say that “50% of doctors are below the median”, and he confirmed this in the aforementioned Twitter conversation; I am disappointed that he justified this mistake by claiming that it would be less understood. I think that a TED audience would know what “median” means, and those who don’t can easily search for its meaning online or in books on their own.
In communicating truth, let’s use the correct vocabulary.