What is the actual use of the median and mode in statistics compared to the average (mean)?
In: Mathematics
The median can be more useful than the mean in situations where there are large extremes at either end of the data set. It’s often helpful in money – let’s say that we’re looking at how much money people have saved up, and we pick 10 people at random for a simplified example. 3 of them have no money in savings, 3 have around $20k saved up, two have $50k, one has $100k, and one has $1million saved. The mean of that set is $126k in savings, but that doesn’t really give us any useful information, because 9/10 of our group actually have less saved up than that, most of them *far* less.
The median of the set, on the other hand, is $20k. Which doesn’t tell us anything about how far the extreme ends are, but it does mean that if we pick an average person, then 50% will fall at or below that amount, and 50% will fall at or above. So it actually tells us a slightly clearer story than the mean – we don’t know how many people have no savings or how many are millionaires, but we do know where the dividing line is.
The mode can also be handy in sets like this – there are two modes in this set, $0, and $20k. The problem with modes in small sets is that they tend to swing frequently, but a mode like $0 definitely tells you a lot of the story in a data set, because it shows you that lots of those empty accounts exist, and that they’re dragging down your other measurements.
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