Statistics Foundation · Lesson 2.4
Shape, skewness and outliers.
Shape describes the full pattern of a distribution. This lesson teaches students how to recognise symmetry, right skew, left skew, long tails, clusters and outliers, then decide whether mean/standard deviation or median/IQR gives the more honest description.
100–105 minute lesson plan
Learn how to describe the whole distribution, not just one number.
Centre, spread and quartiles are powerful, but they can still hide important patterns. Shape helps us decide whether a summary is honest. A graph can reveal skewness, clusters and outliers that a single number may miss.
0–10 min
Why shape matters
Understand that centre and spread are not enough. The overall shape tells us whether data are balanced, skewed, clustered or affected by unusual values.
10–25 min
Symmetry and skewness
Learn how symmetric, right-skewed and left-skewed distributions differ, and how the mean and median respond to skewness.
25–40 min
Tails and unusual values
Study how long tails, heavy tails and extreme observations influence descriptive summaries.
40–60 min
Outlier detection
Use context, graphs and the 1.5 × IQR rule to flag possible outliers without automatically deleting them.
60–85 min
Interactive shape lab
Adjust skewness, tail length, clusters and outlier strength to see how the mean, median, IQR and boxplot change.
85–105 min
Careful interpretation
Practise describing shape in realistic examples such as income, waiting times, exam scores and clinical measurements.
Mastery checklist
By the end, you should be able to diagnose the shape of a dataset.
Explain why shape matters beyond centre and spread.
Recognise symmetric, right-skewed and left-skewed distributions.
Explain how skewness affects the mean and median.
Identify long tails, heavy tails, clusters and gaps.
Use IQR fences to flag possible outliers.
Explain why outliers should be investigated before removal.
Choose summaries that match distribution shape.
Write careful interpretations of shape in context.