# Outlier Calculator

Instructions: Use this outlier calculator by entering your sample data. This calculator will show you all the steps to apply the "1.5 x IQR" rule to detect outliers. These outliers will be shown in a box plot. Please press enter your sample below:

Type the sample (comma or space separated)
Name of the sample (Optional)

#### Outliers Calculator and How to Detect Outliers

What is an outlier? An outlier is a value in a sample that too extreme. Such definition begs to be more precise: What do we mean for being "too extreme"? There are diverse interpretations of this notion of being too extreme. One common rule to decide whether a value in a sample is too extreme is whether or not the value is beyond 1.5 times the Interquartile Range from the first or third quartiles

Mathematically, a value $$X$$ in a sample is an outlier if:

$X < Q_1 - 1.5 \times IQR \, \text{ or } \, X > Q_3 + 1.5 \times IQR$

where $$Q_1$$ is the first quartile, $$Q_3$$ is the third quartile, and $$IQR = Q_3 - Q_1$$

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