mode() — The most common value

Finds the value that shows up the most.

which.max(table(x))

Key idea

• The mode is the value that appears most often in the data. (e.g. mode of 2,2,5,7,7,7 = 7)
• It is the only average that works for categories (like colours), not just numbers. (e.g. colors: red,red,blue -> red)
• Data can have more than one mode when values tie for most frequent. (e.g. 1,1,2,2,3 -> modes 1 and 2)
• If every value appears once, there is no mode. (e.g. 1,2,3,4 -> no mode)
• The mode tells you the most typical or popular choice.

Definition

$$\text{mode}=\arg \underset{x}{\max }\mathrm{freq}(x)$$

$\mathrm{freq}(x)$

how often value x appears

$\arg \max$

the x that makes it largest

In plain words

It is like asking a class “what is everyone’s favorite snack?” — the snack the most kids pick is the mode.

Where you'd use it

• A shop logs the shoe sizes it sells. mode tallies them and finds size 9 appears most often, so that is the size to stock the most of — something an average size could never tell you.
• A class picks favourite colours: blue, red, blue, green, blue. mode returns blue as the most common, working on categories where mean and median make no sense.
• Looking at scores 7, 8, 8, 9, 9, 9, 10, the mode is 9 because it shows up three times — the single most frequent result in the list.

Worked example 2

Some kids’ scores: 7, 8, 8, 9, 9, 9, 10, 10, 11. The score 9 shows up the most, so 9 is the mode.

Frequently asked questions

Does R have a mode() for the most common value?

No — base mode() returns the data type. You need a small custom function.