Practice Outliers (Deep) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

An outlier is a data value that lies unusually far from most other values, potentially indicating measurement error, a rare event, or an important exception.

The weird one that doesn't fit. Is it a mistake, or something interesting?

Example 1

medium
Data: \{12, 15, 14, 13, 16, 14, 15, 85\}. Use the 1.5 \times IQR rule to determine if 85 is an outlier, and discuss whether it should be removed.

Example 2

hard
Calculate the effect of an outlier (value 200) on the mean and median for \{10, 12, 11, 13, 12, 200\}, comparing to the data without the outlier \{10, 12, 11, 13, 12\}.

Example 3

easy
A data set has Q_1 = 50, Q_3 = 70. Determine if each value is an outlier: (a) 85, (b) 15, (c) 105.

Example 4

hard
A researcher finds that removing one outlier changes the correlation from 0.45 to 0.82. Discuss whether the outlier should be removed and what this dramatic change reveals.
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