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outlier

Outlier

A data point that is distinctly separate from the rest of the data. One definition of outlier is any data point more than 1.5 interquartile ranges (IQRs) below the first quartile or above the third quartile.

Note: The IQR definition given here is widely used but is not the last word in determining whether a given number is an outlier.

 

Example:  

For the data 2, 5, 6, 9, 12, we have the following five-number summary:

minimum = 2
first quartile = 3.5
median = 6
third quartile = 10.5
maximum = 12

IQR = 10.5 – 3.5 = 7, so 1.5·IQR = 10.5.

To determine if there are outliers we must consider the numbers that are 1.5·IQR or 10.5 beyond the quartiles.

first quartile – 1.5·IQR = 3.5 – 10.5 = –7
third quartile + 1.5·IQR = 10.5 + 10.5 = 21

Since none of the data are outside the interval from –7 to 21, there are no outliers.

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