# 3.2 - Identifying Outliers: IQR Method

Some observations within a set of data may fall outside the general scope of the other observations. Such observations are called outliers. In Lesson 2.2.2 you identified outliers by looking at a histogram or dotplot. Here, you will learn a more objective method for identifying outliers.

We can use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3. Any values that fall outside of this fence are considered outliers. To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3. This gives us the minimum and maximum fence posts that we compare each observation to. Any observations that are more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers. This is the method that Minitab Express uses to identify outliers by default.

## Example: Test Scores Section

A teacher wants to examine students’ test scores. Their scores are: 74, 88, 78, 90, 94, 90, 84, 90, 98, and 80.

Five number summary: 74, 80, 89, 90, 98.

$$IQR = 90 - 80 = 10$$

The interquartile range is 10.

$$1.5 IQR = 1.5 (10) = 15$$

1.5 times the interquartile range is 15. Our fences will be 15 points below Q1 and 15 points above Q3.

Lower fence: $$80 - 15 = 65$$
Upper fence: $$90 + 15 = 105$$

Any scores that are less than 65 or greater than 105 are outliers. In this case, there are no outliers.

## Example: Books Section

A survey was given to a random sample of 20 sophomore college students. They were asked, “how many textbooks do you own?” Their responses, were: 0, 0, 2, 5, 8, 8, 8, 9, 9, 10, 10, 10, 11, 12, 12, 12, 14, 15, 20, and 25.

The observations are in order from smallest to largest, we can now compute the IQR by finding the median followed by Q1 and Q3.

$$Median = 10$$

$$Q1 = 8$$

$$Q3 = 12$$

$$IQR = 12 - 8 = 4$$

The interquartile range is 4.

$$1.5 IQR = 1.5 (4) = 6$$

1.5 times the interquartile range is 6. Our fences will be 6 points below Q1 and 6 points above Q3.

Lower fence: $$8 - 6 = 2$$
Upper fence: $$12 + 6 = 18$$

Any observations less than 2 books or greater than 18 books are outliers. There are 4 outliers: 0, 0, 20, and 25.