How to Find Outliers Using the Interquartile Range

An outlier is an observation that lies abnormally far away from other values in a dataset. Outliers can be problematic because they can affect the results of an analysis.

One common way to find outliers in a dataset is to use the interquartile range.

The interquartile range, often abbreviated IQR, is the difference between the 25th percentile (Q1) and the 75th percentile (Q3) in a dataset. It measures the spread of the middle 50% of values.

One popular method is to declare an observation to be an outlier if it has a value 1.5 times greater than the IQR or 1.5 times less than the IQR.

Find outliers with IQR

This tutorial provides a step-by-step example of how to find outliers in a dataset using this method.

Step 1: Create the Data

Suppose we have the following dataset:

Step 2: Identify the First and Third Quartile

The first quartile turns out to be 5 and the third quartile turns out to be 20.75.

Thus, the interquartile range turns out to be 20.75 -5 = 15.75.

Step 3: Find the Lower and Upper Limits

The lower limit is calculated as:

Lower limit = Q1 – 1.5*IQR = 5 – 1.5*15.75 = -18.625

And the upper limited is calculated as:

Upper limit = Q3 + 1.5*IQR = 20.75 + 1.5*15.75 = 44.375

Find outliers with IQR method

Step 4: Identify the Outliers

The only observation in the dataset with a value less than the lower limit or greater than the upper limit is 46. Thus, this is the only outlier in this dataset.

Example of finding outliers with the interquartile range

Note: You can use this Outlier Boundary Calculator to automatically find the upper and lower boundaries for outliers in a given dataset.

How to Find Outliers in Practice

The following tutorials explain how to find outliers using the interquartile range in different statistical software:

How to Find Outliers in Excel
How to Find Outliers in R
How to Find Outliers in Python
How to Find Outliers in SPSS

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