Mean, Median and Mode

Three ways of naming a 'typical' value, and why the choice changes the story.

Also known as: mean, median, mode, average

Three numbers compete to describe a “typical” value, and on messy data they say different things.

The mean is the sum divided by the count.
The median is the middle value once the data is sorted.
The mode is the value that appears most often.

Take a column of last month’s order values (illustrative):

12, 15, 15, 16, 18, 19, 20, 21, 430

The mean is about 63. The median is 18. The mode is 15. If you tell your stakeholder “the average order was 63”, and most customers spend about 15, you have described a number that no customer produced.

Which one to reach for:

Use the mean when the distribution is roughly balanced and a total makes sense. It uses every data point, which is both its strength and its weakness.
Use the median when a few very large or very small values would drag the mean. It is the usual choice for response times, salaries and order values.
Use the mode when the question is about the most common category or the most frequent value, not a typical size.

One trap worth memorising: an average of averages is not the average. Averaging a per-region average only gives the overall average when every region has the same number of rows. Combine the sums and the counts instead, which is what GROUP BY aggregation should do in the first place.

Look at the shape before you pick: distribution shapes tells you whether the mean is being honest, and outliers tells you whether one row is doing all the work. For a skewed column, the median and a percentile are usually the better report.