Statistics / Unit 2: Describing Distributions
2.4 Outliers and the 1.5 IQR Rule
Notes
An outlier is a value that falls far from the rest. The 1.5 IQR rule gives a standard test.
- Lower fence $= Q_1 - 1.5 \times \text{IQR}$. Upper fence $= Q_3 + 1.5 \times \text{IQR}$.
- A value beyond either fence is an outlier.
- Example: $Q_1 = 20$, $Q_3 = 30$, IQR $= 10$. Fences: $20 - 15 = 5$ and $30 + 15 = 45$. The value 50 is an outlier.
- Always investigate outliers: they may be errors or genuinely unusual cases.
Practice
A data set has $Q_1 = 12$ and $Q_3 = 20$. Which value is an outlier by the 1.5 IQR rule?
IQR $= 8$, $1.5 \times 8 = 12$. Fences: $12 - 12 = 0$ and $20 + 12 = 32$. Only 35 is outside.
A data set has $Q_1 = 40$ and $Q_3 = 52$. The upper fence is:
IQR $= 12$, $1.5 \times 12 = 18$, and $52 + 18 = 70$.
Which pair of statistics is resistant to (not much affected by) outliers?
Both the median and IQR depend on positions in the ordered list, not on extreme values.
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