What is an outlier?
Big Idea: An outlier is a data value that is much larger or much smaller than the other values in the dataset. Unusual or extreme.
| Example data | Outlier? | Why? |
|---|---|---|
| 85, 87, 89, 91, 93 | No | All close together |
| 85, 87, 89, 91, 150 | Yes | 150 much larger |
| 2, 3, 4, 5, 6 | No | All consecutive |
| 2, 3, 4, 5, −50 | Yes | −50 much smaller |
Causes of outliers
Legitimate: Real extreme values: World records, rare events. Keep.
Error: Measurement mistakes, wrong units. Investigate and consider removing.
Key point: Never blindly remove outliers. Investigate first.
Worked example - Causes of outliers
Apply the core method for Data Reliability and Outliers in this section context.
Step by step
- Write the relevant formula or rule first to secure method marks.
- Substitute values from the question carefully and keep units/labels clear.
- Simplify and check whether the result is reasonable in context.
Final answer
Final answer should be clearly stated and interpreted for Data Reliability and Outliers.
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IQR method for identifying outliers
Worked example
Data: 12, 14, 15, 16, 18, 19, 20, 21, 25, 45 Identify outliers.
Solution
- Q1 = 14.75, Q3 = 21.25, IQR = 6.5
- Lower bound = 14.75 − 1.5(6.5) = 5
- Upper bound = 21.25 + 1.5(6.5) = 31
- 45 > 31, so 45 is outlier
Final answer
Outlier: 45
How outliers affect statistics
| Statistic | Outlier effect |
|---|---|
| Mean | Highly affected |
| Median | Resistant |
| Range | Highly affected |
| IQR | Resistant |
| SD | Highly affected |
Strategy: With outliers: Use median and IQR. Without: Can use mean and SD.