6. Percentiles and Quartiles

6.2 Finding Outliers Using Quartiles

We can use quartiles to identify outliers or data points that are wildly discrepant with the rest of the data. For this application, we need another definition of data dispersion :

    \[ \textrm{Interquartile Range} = IQR = Q_3 - Q_1 \]

With the IQR any data value that satisfies:

(a) less than Q_1 - (1.5 \times IQR)
or
(b) greater than Q_3 + (1.5 \times IQR)

…is considered an outlier. This is one of many ways one can define an outlier. As we will discuss below, it is a robust way of identifying outliers.

Example 6.4 : Consider the data of Example 6.2. We found

    \[ Q_{1} = 9 \hspace{.25in} Q_{2} = 14 \hspace{.25in} Q_{3} = 20 \]

so,

    \[ IQR = Q_{3} - Q_{1} = 20 - 9 = 11. \]

Following our rules for finding outliers, we compute:

(a) lower acceptable value limit

= Q_{1} - (1.5 \times IQR)
= 9 - (1.5 \times 11)
= 9 - 16.5 = −7.5

(b) upper acceptable value limit

= Q_{3} + (1.5 \times IQR)
= 20 + (1.5 \times 11)
= 20 + 16.5 = 36.5

and 50 > 36.5 so 50 is considered an outlier.

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Introduction to Applied Statistics for Psychology Students Copyright © 2022 by Gordon E. Sarty is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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