Outliers
Master Outliers for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. Outliers are extreme values, often identified as more than 1.5 times the IQR beyond the quartiles.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
An outlier is a value that lies far outside the pattern of the rest of the data. Identifying them formally requires a rule rather than a judgement by eye. This is a Higher-only topic.
The quartile rule defines an outlier as any value more than \(1.5 \times \text{IQR}\) below the lower quartile or above the upper quartile. So the boundaries are \(Q_1 - 1.5 \times \text{IQR}\) and \(Q_3 + 1.5 \times \text{IQR}\).
An alternative rule uses the mean and standard deviation, treating any value more than two standard deviations from the mean as an outlier. Once identified, an outlier should only be removed if it is an error — a genuine extreme value should be kept, and removing it would misrepresent the data.
Revision notes
The quartile rule
An outlier is any value below \(Q_1 - 1.5 \times \text{IQR}\) or above \(Q_3 + 1.5 \times \text{IQR}\).
Calculate the interquartile range first, multiply by 1.5, then find both boundaries. Any value outside them is an outlier.
The standard deviation rule
An outlier is any value more than two standard deviations from the mean.
The boundaries are \(\bar{x} - 2\sigma\) and \(\bar{x} + 2\sigma\). This rule is used when the mean and standard deviation are already known.
What to do with an outlier
Remove it only if it is a genuine error, such as a transcription mistake or an impossible value.
A genuine extreme value should be kept, because removing it would misrepresent the true spread of the data. Always state the reason for any removal.
Key points
- An outlier lies far outside the pattern.
- Quartile rule uses \(1.5 \times \text{IQR}\).
- Boundaries are \(Q_1 - 1.5 \times \text{IQR}\) and \(Q_3 + 1.5 \times \text{IQR}\).
- The alternative rule uses two standard deviations.
- Remove an outlier only if it is an error.
- Genuine extreme values should be kept.
Worked examples
Example 1
A data set has \(Q_1 = 20\), \(Q_3 = 32\). Work out the upper boundary for outliers. [3 marks]
Working
Example 2
A data set has mean 40 and standard deviation 6. Work out the lower boundary using the two standard deviation rule. [2 marks]
Working
Example 3
Explain when an outlier should be removed from a data set. [2 marks]
Working
Common mistakes
Using \(1.5 \times Q_1\) instead of \(1.5 \times \text{IQR}\).
The multiplier applies to the interquartile range, not the quartile.
Removing every outlier automatically.
Only errors should be removed; genuine extremes are kept.
Adding when you should subtract.
Subtract for the lower boundary, add for the upper.
Forgetting to calculate the IQR first.
It is needed before either boundary can be found.
Exam tips
- Calculate the IQR as your first step.
- Show the multiplication by 1.5 separately.
- Justify any decision to remove or keep an outlier.
- Remember this is a Higher-only topic.
Key terms
- Outlier
- A value far outside the pattern of the data.
- Quartile rule
- Identifying outliers using \(1.5 \times \text{IQR}\).
- Boundary
- The limit beyond which a value is an outlier.
- Transcription error
- A mistyped value, which justifies removal.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.