**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:

## Outlier 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

This outlier calculator will show you all the steps and work required to detect the outliers: First, the quartiles will be computed, and then the interquartile range will be used to assess the threshold points used in the lower and upper tail for outliers.

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 \(IQR = Q_3 - Q_1\)

Outliers need to be analyzed because their presence may invalidate the results of many statistical procedures. Outliers also need to be analyzed because often times they arise due to typing errors.

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