**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:

#### 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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