# How to Find the Mode or Modal Value

The mode is simply the number which appears **most often**.

## Finding the Mode

To find the
mode, or modal value, first put the numbers **in order**, then count how many of each number. A number that appears **most often** is the **mode**.

### Example:

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

**In order** these numbers are:

3, 5, 7, 12, 13, 14, 20, **23, 23, 23, 23**, 29, 39, 40, 56

This makes it easy to see which numbers appear **most often**.

In this case the mode is **23**.

### Another Example: {19, 8, 29, 35, 19, 28, 15}

Arrange them in order: **{8, 15, 19, 19, 28, 29, 35}**

19 appears twice, all the rest appear only once, so **19 is the mode**.

*How to remember? Think "mode is most"*

## More Than One Mode

We can have more than one mode.

### Example: {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}

3 appears three times, as does 6.

So there are two modes: at **3** and **6**

Having two modes is called **"bimodal"**.

Having more than two modes is called **"multimodal"**.

## Grouping

When all values appear the same number of times the idea of a mode is not useful. But we could group them to see if one group has more than the others.

### Example: {4, 7, 11, 16, 20, 22, 25, 26, 33}

Each value occurs once, so let us try to group them.

We can try groups of 10:

- 0-9:
**2 values**(4 and 7) - 10-19:
**2 values**(11 and 16) - 20-29:
**4 values**(20, 22, 25 and 26) - 30-39:
**1 value**(33)

In groups of 10, the "20s" appear most often, so we could choose 25 as the mode.

You could use different groupings and get a different answer!

Grouping also helps to find what the typical values are when the real world messes things up!

### Example: How long to fill a pallet?

Philip recorded how long it takes to fill a pallet in minutes:

{35, 36, 32, 42, 58, 56, 35, 39, 46, 47, 34, 37}

It takes longer if there is break time or lunch so an average is not very useful.

But grouping by 5s gives:

- 30-34:
**2** - 35-39:
**5** - 40-44:
**1** - 45-49:
**2** - 50-54:
**0** - 54-59:
**2**

"35-39" appear most often, so we can say it normally takes **about 37 minutes **to fill a pallet.