Mode (most frequent value)

The mode is the value that appears most often in the list.

Idea

To find the mode, count how many times each distinct value appears. The value with the highest count is the mode.

Example: $4, 6, 4, 7, 8, 4, 6$. Counts: $4$ appears $3$ times; $6$ appears $2$ times; $7, 8$ once each. Mode $= 4$.

A list can have:

• One mode (unimodal): one most frequent value.
• Two modes (bimodal): two values tied for the highest count.
• No mode: when every value appears the same number of times.

Example of bimodal: $1, 2, 2, 3, 4, 4, 5$. Both $2$ and $4$ appear twice. Modes: $2$ and $4$.

Why mode? It is the most popular value , useful when you care about the most common case. Examples:

• Shoe sizes (a shop wants to stock the most popular size).
• Bus arrival times (the most common arrival).
• Survey answers (the most common opinion).

Mode is good for categorical data (where mean and median don't make sense), most-popular items, modes of fashion.

Worked examples

Example 1. Mode of $3, 5, 3, 7, 9, 3$.

$3$ appears $3$ times, others once. Mode $= 3$.

Example 2. Mode of $1, 2, 3, 4, 5$ (each unique).

No mode (or "every value is a mode" depending on convention).

Example 3. Bimodal: $7, 7, 8, 9, 9, 10$. Modes?

$7$ and $9$ each appear twice. Bimodal: modes $7$ and $9$.

Example 4. Shoe sizes sold: $7, 8, 8, 9, 10, 8, 7, 9, 11, 8$. Mode?

$8$ appears $4$ times, $7$ twice, $9$ twice, $10$ once, $11$ once. Mode $= 8$.

Try it yourself

1. Mode of $2, 4, 4, 6, 6, 6, 8$.
2. Mode of $1, 1, 2, 3, 3$.
3. Mode of $5, 10, 15, 20, 25$.
4. Mode of $a, b, a, c, b, a, d$ (where letters represent categories).
5. Shoe sizes: $6, 7, 6, 8, 7, 6, 9, 6$. Mode?
6. Marks of $10$ students: $35, 50, 50, 70, 80, 90, 50, 70, 50, 60$. Mode?
7. Daily temperatures: $30, 30, 31, 32, 31, 30, 32$. Mode?
8. Birth months of $12$ classmates: $4, 5, 4, 7, 4, 8, 4, 5, 6, 9, 5, 4$. Mode?

Activity

Collect the most-favoured snack (one word answer) from $20$ classmates. The mode tells you the most popular snack.