# AP Statistics : How to find outliers

## Example Questions

### Example Question #1 : How To Find Outliers

Use the following five number summary to determine if there are any outliers in the data set:

Minimum:

Q1:

Median:

Q3:

Maximum:

It is not possible to determine if there are outliers based on the information given.

There is at least one outlier on the high end of the distribution and at least one outlier on the low end of the distribution.

There is at least one outlier on the high end of the distribution and no outliers on the low end of the distribution.

There are no outliers.

There is at least one outlier on the low end of the distribution and no outliers on the high end of the distribution.

There are no outliers.

Explanation:

An observation is an outlier if it falls more than  above the upper quartile or more than  below the lower quartile.

. The minimum value is  so there are no outliers in the low end of the distribution.

. The maximum value is  so there are no outliers in the high end of the distribution.

### Example Question #1 : How To Find Outliers

For a data set, the first quartile is , the third quartile is and the median is .

Based on this information, a new observation can be considered an outlier if it is greater than what?

Explanation:

Use the  criteria:

This states that anything less than  or greater than  will be an outlier.

Thus, we want to find

where .

Therefore, any new observation greater than 115 can be considered an outlier.

### Example Question #1 : How To Find Outliers

You are given the following information regarding a particular data set:

Q1:

Q3:

Assume that the numbers  and  are in the data set. How many of these numbers are outliers?

None of the numbers are outliers

Three

Two

Four

One

Two

Explanation:

In order to find the outliers, we can use the  and  formulas.

Only two numbers are outside of the calculated range and therefore are outliers:  and .

### Example Question #1 : How To Find Outliers

Use the following five number summary to answer the question below:

Min:

Q1:

Med:

Q3:

Max:

Which of the following is true regarding outliers?

There is only one outlier in this entire data set.

There are no outliers in this data set.

There are no outliers in the upper side of the data set, but there is at least one outlier on the lower side of the data set.

There is at least one outlier in the lower side of the data set and at least one outlier in the upper side of the data set.

There are no outliers in the lower side of the data set, but there is at least one outlier on the upper side of the data set.

There is at least one outlier in the lower side of the data set and at least one outlier in the upper side of the data set.

Explanation:

Using the  and  formulas, we can determine that both the minimum and maximum values of the data set are outliers.

This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.

### Example Question #1 : How To Find Outliers

Which values in the above data set are outliers?

no outliers

Explanation:

Step 1: Recall the definition of an outlier as any value in a data set that is greater than  or less than .

Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or . To find  and , first write the data in ascending order.

. Then, find the median, which is  . Next, Find the median of data below , which is  . Do the same for the data above  to get . By finding the medians of the lower and upper halves of the data, you are able to find the value,  that is greater than 25% of the data and , the value greater than 75% of the data.

Step 3: . No values less than 64.

. In the data set, 105 > 104, so it is an outlier.

### Example Question #6 : How To Find Outliers

A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?