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S3.1StatisticsCore

Outliers

An outlier is a value that lies far from the rest of the data. There are two standard tests for spotting them — a quartile-based rule and a mean/standard-deviation rule — and a clear procedure for deciding what to do with them.

20 min Representations of Data
Edexcel AS Level Maths: 3.1 OutliersCurated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Define an outlier
  • Use the 1.5 × IQR rule
  • Use the mean ± 2 standard deviations rule
  • Decide whether to keep or clean an outlier
1

The quartile (IQR) rule

A common rule flags a value as an outlier if it is more than 1.5×IQR1.5 \times \text{IQR} below Q1Q_1 or above Q3Q_3. The multiplier is sometimes given as a different number in a question — always use the one stated.

x<Q1−1.5 IQRorx>Q3+1.5 IQRx < Q_1 - 1.5\,\text{IQR} \quad \text{or} \quad x > Q_3 + 1.5\,\text{IQR}
Outside these fences ⟶ outlier.
Example 1If Q1=10Q_1 = 10, Q3=20Q_3 = 20, is x=38x = 38 an outlier (1.5 × IQR rule)?
1IQR =10= 10; upper fence =20+15=35= 20 + 15 = 35.
238>3538 > 35.
Answeryes, an outlier
2

The mean/standard-deviation rule

An alternative rule flags values more than 22 standard deviations from the mean — outside xˉ±2σ\bar{x} \pm 2\sigma. Use whichever rule the question specifies.

x<xˉ−2σorx>xˉ+2σx < \bar{x} - 2\sigma \quad \text{or} \quad x > \bar{x} + 2\sigma
More than 2 standard deviations from the mean.
3

Cleaning data

Once identified, an outlier may be a genuine value or an error. Cleaning\textbf{Cleaning} means removing values that are clearly errors. Never remove a value just because it is extreme — only if there is a reason to believe it is wrong.

Tip — Extreme ≠ wrong. Only remove an outlier if there’s justification that it’s an error.

Formula recap

Q1−1.5 IQR, Q3+1.5 IQRQ_1 - 1.5\,\text{IQR}, \ Q_3 + 1.5\,\text{IQR}
Quartile outlier fences.
xˉ±2σ\bar{x} \pm 2\sigma
Mean/SD outlier rule.

Common mistakes to avoid

Assuming the multiplier is always 1.5.
Use whatever multiple the question gives (it varies).
Deleting every outlier automatically.
Only clean values that are genuinely errors.

Key takeaways

  • Quartile rule: outside Q₁ − 1.5·IQR or Q₃ + 1.5·IQR.
  • Mean/SD rule: outside x̄ ± 2σ.
  • Clean (remove) only outliers that are clearly errors.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Check your understanding

Work through questions on Outliers. Use the feedback to decide what needs another look.

1 past-paper question · 1 mark

Practise this topic

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