Mode

The mode is just the most common value in a data set.
It’s the value that appears most often.

Calculating mode

1. Count how many times each value appears in the data set.
2. The value that appears the largest number of times is the mode.

Basically:

The mode is the most common value in a data set.

Bimodal, trimodal and beyond

Sometimes, we won’t have a single value that appears more often than all the others. For example, in this dataset.

\{1, 1, 2, 2, 3\}

Both 1 and 2 appear twice, which is more than any other value. So, this dataset actually has two modes: 1 and 2.

• When there are two modes, we call the dataset “bimodal”.
• When there are three modes, we call the dataset “trimodal”.
• When there are more than three modes, we just call the dataset “multimodal”.

No mode

If all the values in a dataset appear the same number of times, then there is no mode. For example, in this dataset:

\{1, 1, 8, 8, 4, 4\}

We just say ‘no mode’.

Examples

Find the mode of \{2, 3, 5, 7, 11\}

• Each value appears only once, so there is no mode.
• Answer: no mode

Find the mode of \{1, 4, 9, 16, 16, 25\}

• 16 appears twice, which is more than any other value.
• Answer: 16

Find the mode of \{3, 1, 4, 1, 5, 9\}

• 1 appears twice, which is more than any other value.
• Answer: 1

Find the mode of \{1, 3, 3, 4, 5, 5, 7, 8\}

• Both 3 and 5 appear twice, which is more than any other value.
• Answer: 3 and 5 (bimodal)

Find the mode of \{1, 1, 3, 4, 4, 5, 6, 8, 8, 9\}

• 1, 4 and 8 all appear twice, which is more than any other value.
• Answer: 1, 4 and 8 (trimodal)