Uses and Pitfalls
Mean versus Median: When to Use Which for a Representative Typical Value?
The median is a better choice when…
… the indicator is susceptible to a small number of extreme values, or outliers. Example 2 offers a good illustration. Lora and Tobias earned much more than the rest and their wages were included in the calculation of the mean wage, making it less representative of the typical observation. On the other hand, the median, capturing only the middle value, is not affected by these outliers. It gives us a better estimate of the typical wage. However, this also means the presence of Lora’s and Tobias’ relatively higher wages are hidden.
Diagram from Example 2
The mean is a better choice when…
… there are no extreme values which might affect it. The mean offers a better summary of all values as it includes information from every observation, rather than just the middle value. If Lora and Tobias now earn wages closer to the rest, say $6,000 each, the median remains at $3,920 while the mean becomes $3,914.
As the mean holds more information than the median, we will also be able to derive the sum of all the observations, for example the total income paid by an employer, when the number of observations is provided.