# 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.

“average” seems to have a vague definition. according to wikipedia, http://en.wikipedia.org/wiki/Average, “the word “average” can be used to refer to the median, the mode, or some other central or typical value”

Hi Wei,

I have never encountered anybody who uses “average” to denote the median, the mode, or any statistic other than the mean.

Specificity in language is necessary and useful in conveying the truth.

My sense is that when many average people, even average journalists, talk or write about average income, they are referring to the median. Yes, it is confusing. So… If one means the mean, say the mean; don’t say average.

I also suspect that Kohn was trying to be just a bit humorous, playing on the vague meanings of average.

Hi Michael,

Thanks for sharing your views. Given how often the average is used in everyday life, it’s hard to imagine the general public being confused about what “average” means.

– “The average score on the test was 68%.”

– “Kevin Durant average 32.0 points per game in the 2013-2014 season.”

– “On average, there are 1.6 dogs per household in Canada.”

I think that most people would understand what the average means in these examples, and I doubt that they would confuse it with the median.