Continuous education

# Be careful for the mean tricks of the mean

Readers of this article might understand – on average – 80% of everything that follows. It is well possible that a majority of the readers understand less than the mean reader does. Say what? Did we already lose you? There is no reason to be overly concerned. Means (also known as averages) can be tricky and most people, even college educated professionals, will easily fall prey to their possible deception.

Communications professionals would do well to understand where lie the dangers so they can be numbers savvy enough whenever they need to analyze and communicate on the mean of  any set of data.

### Calculating the mean

The mean of a series of numbers makes for an easy equation. You add up the scores and divide them by the number of scores. If Paul, Tom and Lisa score 4, 5 and 6 respectively on a test, then the mean score on the test amounts to 5. In this case the mean is actually one of the measured scores, but that is a coincidence, it does not have to be that way.  All of this basic high school algebra. So far so good. Let’s turn it up a notch now.

### Deceiving means: the median to the rescue

In any series of scores there is always the risk that a small set (thus an not representative sample) of extreme scores make the mean turn up to be (much) higher or lower than the median score.  The median score is the value that divides the set of measured values in half. 50% of everybody has a score lower than the median and 50% has one higher. In the case of an even amount of values, the median is the average of the middle two scores. If Paul, Tom, Lisa and Ellen score 2, 5, 6 and 14 on a test, the median score is 5.5.

Take a close look now at the mean in our example. Ellen had such a high score that her score put the mean on 6.75. Paul and Tom scored lower than the median. Three people (Paul, Tom and Lisa, amounting to 75% of the students) scored lower than the mean. So, medians are often a much better way to gauge the distribution of scores in a population than means are because they are much more resilient to outlier scores.

### Stephen Jay Gould beats the median

The renowned paleontologist Stephen Jay Gould was diagnosed in 1982 with peritoneal mesothelioma. In an article in Discover in 1985 he wrote about how his statistical knowledge had helped him understand what he could reasonably expect. The median time of survival for anyone with his diagnosis was 8 months. In other words: half of the patients lived to be less than 8 months and another half lived to be more than 8 months. Given the early stage of the diagnoses he thought that he would probably be part of the second group. But how long could he possibly expect to then still have to live? He couldn’t know, but it was very much possible that there were still quite a lot of years ahead of him. There was no inherent reason to think that a median of 8 months would come with a maximum time of survival of 16 months.   Gould was not wrong in his optimistic assessment and lived for another 20 years after receiving the diagnosis.