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 Video by Zeeshan Zamurred Representations of Data

Edexcel AS Level Maths: 3.1 OutliersWatch the full walkthrough before the notes below.

Open on YouTube

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

The quartile (IQR) rule

A common rule flags a value as an outlier if it is more than $1.5 \times IQR$ below $Q_{1}$ or above $Q_{3}$ . The multiplier is sometimes given as a different number in a question — always use the one stated.

x < Q_{1} - 1.5 IQR or x > Q_{3} + 1.5 IQR

Outside these fences ⟶ outlier.

1IQR

= 10

; upper fence

= 20 + 15 = 35

38 > 35

Answeryes, an outlier

The mean/standard-deviation rule

An alternative rule flags values more than $2$ standard deviations from the mean — outside $\overset{x}{ˉ} \pm 2 σ$ . Use whichever rule the question specifies.

x < \overset{x}{ˉ} - 2 σ or x > \overset{x}{ˉ} + 2 σ

More than 2 standard deviations from the mean.

Cleaning data

Once identified, an outlier may be a genuine value or an error. $Cleaning$ 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

Q_{1} - 1.5 IQR, Q_{3} + 1.5 IQR

Quartile outlier fences.

\overset{x}{ˉ} \pm 2 σ

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

Ready to lock in Outliers? Pick a mode and earn XP & Dobloons.