Three ways to say “typical”
When someone reports “the average”, they are trying to describe a whole set of numbers with one figure. But there is more than one way to do that. The three most common are the mean, the median and the mode. They often give different answers for the same data, and each has situations where it is the better description.
Throughout this article we use a small, hypothetical data set: the number of minutes five parcels were late, recorded as 2, 3, 3, 4 and 18.
The mean
The mean is what most people think of as the average. Add all the values and divide by how many there are.
For the parcels: 2 + 3 + 3 + 4 + 18 = 30. There are 5 values, so the mean is 30 ÷ 5 = 6 minutes.
The mean uses every value, which is its strength. It is also the reason it is sensitive to extreme values. The late parcel (18 minutes) pulled the mean up to 6, even though four of the five parcels were 4 minutes late or less.
The median
The median is the middle value when the data are arranged in order. For an odd number of values, it is the one in the center. For our ordered list 2, 3, 3, 4, 18, the middle value is 3, so the median is 3 minutes.
For an even number of values, there are two middle numbers, and the median is the value halfway between them. For 2, 4, 6, 8 the middle two are 4 and 6, so the median is 5.
The median is not much affected by outliers. If the last parcel had been 180 minutes late instead of 18, the median would still be 3. This makes it a common choice when a few extreme values could distort the picture.
A tip: always sort the data first. Picking the middle of an unsorted list is a frequent error.
The mode
The mode is the value that appears most often. In 2, 3, 3, 4, 18 the number 3 appears twice and every other value once, so the mode is 3.
A data set can have more than one mode (for example 1, 1, 2, 3, 3 has modes 1 and 3), or none at all if every value appears equally often. The mode is the only one of the three that also works for categories. If you ask people their favorite color, you cannot add up “blue” and “green” to get a mean, but you can say which was chosen most often.
Comparing them on the same data
| Measure | Result for 2, 3, 3, 4, 18 | What it reflects |
|---|---|---|
| Mean | 6 | Every value, including the outlier |
| Median | 3 | The middle position |
| Mode | 3 | The most frequent value |
None of these is wrong. They answer different questions. The mean answers “if the total were shared out equally, what would each get?” The median answers “what is the middle case?” The mode answers “what is most common?” For the parcels, saying the typical delay was 3 minutes feels more honest than saying 6, because most parcels were nowhere near 6 minutes late.
When each works best
The mean is a good choice when the data are fairly symmetric, with no extreme values, and when you care about the total. Test scores in a large class, or daily temperatures across a month, are often summarized by the mean.
The median suits skewed data, where a few very large or very small values would drag the mean away from the typical case. Incomes and house prices are commonly described by their median for this reason, since a few very high values can raise the mean well above what most people experience.
The mode is best for categories or for finding the most popular option, such as the most common shoe size sold in a shop.
When the mean is much higher than the median, that usually suggests a few large values pulling the mean upward. Comparing the two is a quick way to spot a skewed set.
Reading averages critically
A single average hides how spread out the values are. Two classes could both have a mean of 70 on a test, yet one could have everyone near 70 while the other has scores from 30 to 100. Reporting the range (largest minus smallest) alongside an average gives a fuller picture. For our parcels, the range is 18 − 2 = 16 minutes.
Statistics in news and marketing sometimes pick whichever average makes a point most dramatically, so developing information literacy includes asking which average was used and why. A summary on its own also does not show a cause for any pattern, a point made in the article on correlation causation.
Doing it in practice
Most spreadsheets have built-in functions for all three, commonly called AVERAGE, MEDIAN and MODE, so the calculation is rarely a problem. The harder part is choosing the right one and interpreting it. If you are working through spreadsheet basics, try entering the parcel data and comparing results. Then plot the values with basic charts, such as a simple bar chart or dot plot, to see the outlier directly. Seeing the shape of the data often tells you more than any single figure.