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The interquartile range (IQR) is a powerful tool for identifying outliers, which are data points that are significantly different from the rest of the data set. Outliers can be detected by finding the difference between the 75th percentile (Q3) and the 25th percentile (Q1). The IQR is calculated by subtracting Q1 from Q3. Any data points that lie more than 1.5 times the IQR below Q1 or above Q3 are considered potential outliers. This method can be used to quickly identify outliers in a data set.
An outlier is an 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.
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:
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.
Note: You can use this 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: