# Mode

Mode is a measure of central tendency -- it's a number that can summarize a set of data or a group of numbers.

**The mode of a set of numbers is the number that appears the most often.**

Mode is the simplest measure of central tendency. It's also the one that is most likely to be not very useful -- so know how to find it and what it means, but don't rely on it exclusively (always figure out the median and mean also if you're trying to learn something about a set of data).

**How do you find a mode?**

Look at your dataset. Presume you have earned the following grades on math tests this semester

$79$, $81$, $83$, $70$, $95$, $83$, $79$, $55$, $99$, $89$, $83$

You don't have to put the numbers in order, but it's a good idea to do so. Putting the numbers in order makes it very easy to see which numbers occur most often.

$55$, $70$, $79$, $79$, $81$, $83$, $83$, $83$, $89$, $95$, $99$

Then, you find the number that occurs most often:

$55$, $70$, $79$, $79$, $81$, $\underline{83}$, $\underline{83}$, $\underline{83}$, $89$, $95$, $99$

The mode of this set of numbers is: $83$

There is only one important rule to remember about modes: **you can have more than one mode**. If more than one number appears the most number of times, both of those numbers are modes of the dataset.

Let's say you had on additional score in your set of test scores:

$79$, $81$, $83$, $70$, $95$, $83$, $79$, $55$, $99$, $89$, $83$, $79$

Put them in order:

$55$, $70$, $79$, $79$, $79$, $81$, $83$, $83$, $83$, $89$, $95$, $99$

You'll see that both $79$ and $83$ appear three times:

$55$, $70$, $\underline{79}$, $\underline{79}$, $\underline{79}$, $81$, $\underline{83}$, $\underline{83}$, $\underline{83}$, $89$, $95$, $99$

Three times is the MOST times that any number appears. So, both $79$ and $83$ are modes of this dataset.

Overall, the mode of a dataset is the number (or numbers) that appear the most times in the dataset.

#### Practice Problems:

## Mode

Find the mode of each data set.

1. 14, 13, 20, 24, 15, 10, 22, 18

2. 9, 7, 4, 9, 4, 10, 5, 14, 9, 4

3. 80, 65, 92, 77, 65, 10, 80, 65

4. 14.94, 18.74, 19.99, 19.99, 29.49

5. 13, 18, 13, 14, 13, 16, 14, 21, 13

6. 17, 77, 20, 15, 84, 15, 57, 67

7. 86, 30, 82, 86, 20, 79, 52, 93

8. 38, 90, 12, 98, 51, 77, 22, 36

9. 69, 11, 28, 98, 81, 29, 44, 40

10. 81, 73, 88, 48, 84, 88, 81, 88

11. 0.25, .075, 0.25, 0.50, 2.25

12. 33, 11, 18, 18, 33, 18, 23, 33

#### Answer Key: