Median & mode

If almost everyone in a group earns little and just one person is a millionaire, the average wage would be dishonestly high. The mean, the sum of all values divided by how many there are, is easily thrown off course by single extreme values. That is why there are two more measures that often hit the middle more honestly: the median and the mode.

The median: the middle

For the median you first sort all values by size. The median is then the value standing exactly in the middle. In 3, 4, 7 the 4 is the median. If the number of values is even, there is no single middle: then you take the mean of the two middle numbers, so for 1, 4, 6, 9 the mean of 4 and 6, which is 5.

The mode: the most frequent

The mode is the value that appears most often. For shoe sizes 37, 38, 38, 39 the mode is 38, because it shows up twice. It is the only one of the three measures that also works where you cannot compute with the values, such as the most popular colour in a survey. If two values tie for the lead, there are two modes, and if every value appears just once, there is none.

Robust against outliers

This is exactly where the median shines. Take the values 4, 5, 6, 7 plus an outlier of 100. The mean jumps to 24.4, even though four of the five values are single digits. The median, in contrast, comes out at 6, because it depends only on which value sits in the middle of the sorted row, not on how large the largest one is. Even if the 100 turned into a million, the median would still be 6.

Which measure when?

If the values are spread evenly, the mean fits well. If there are single outliers, the median is more honest. And when it is about categories instead of numbers, only the mode helps. Often it is best to look at all three and compare what they tell you.