Median vs mean: when a single number lies

When you have hundreds of values in a table, you want to summarise them with a single number: a "typical salary", a "usual response time", an "average price". Such a number is called a measure of location.

The best known is the arithmetic mean: you add up all the values and divide by their count.

$$\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{1}{n}\sum_{i=1}^{n} x_i$$

where $\bar{x}$ is the mean, $x_i$ is the i-th value, $n$ is the number of values and $\sum$ stands for the sum.

Tip: The mean "sees" every value. That is its strength, but also its weakness. In a moment you will see why.