Outlier

Outlier is an extremely high or an extremely low data value when compared with the rest of the data values.

Rule of thumb: an outlier is is a value that is 1 and a half the length of the interquartile range either below \(Q_1\) or above \(Q_3\), that is as a good bench mark we consider outliers to be values that are farther from \(Q_1\) or \(Q_3\) than they are from each other.

An outlier can strongly affect the mean and standard deviation of a variable. For example, suppose a researcher mistakenly recorded an extremely high data value. This value would then make the mean and standard deviation of the variable much larger than they really were.

Identify an outlier:

Step 1

Arrange the data in order from lowest to highest and find \(Q_1\) and \(Q_3\)

Step 2

Find the interquartile range:

\[\text{IQR}=Q_3-Q_1\]

Step 3

Multiply the IQR by 1.5

Step 4

Subtract the value obtained in step 3 from \(Q_1\) and add the value obtained in step 3 to \(Q_3\)

Step 5

Check the data set for any data value that is smaller than \(Q_1-1.5\cdot(\text{IQR})\) or larger than \(Q_3+1.5\cdot(\text{IQR})\)