Statistics Foundation · Lesson 2.3
Quartiles, percentiles and five-number summaries.
Quartiles and percentiles describe where values sit inside an ordered dataset. This lesson teaches students how to sort data, interpret positional summaries, calculate quartiles, understand percentile rank, build five-number summaries, read boxplots and use IQR fences to flag possible outliers.
100–105 minute lesson plan
Learn how position summarises a distribution.
Measures of centre and spread are stronger when we understand position. Quartiles and percentiles let us describe how values are arranged from low to high. They are especially useful for skewed data, ordinal data, boxplots and robust summaries.
0–10 min
Why positions matter
Understand that ordered data can be described by location in the list, not only by arithmetic calculations.
10–25 min
Ranks, positions and ordered data
Learn how sorting values helps us identify the minimum, maximum, median, quartiles and percentiles.
25–45 min
Quartiles and the IQR
Study Q1, Q2 and Q3 as position-based summaries, and connect them to the interquartile range.
45–60 min
Percentiles
Learn how percentiles divide ordered data into 100 parts and how to interpret percentile statements carefully.
60–85 min
Five-number summaries and boxplots
Bring minimum, Q1, median, Q3 and maximum together into a compact summary and visualise it with a boxplot.
85–105 min
Outlier fences and interpretation
Use the 1.5 × IQR rule to flag unusually low or high values, then practise writing careful interpretations.
Mastery checklist
By the end, you should be able to read a boxplot like a statistical story.
Order a dataset from smallest to largest.
Explain Q1, Q2 and Q3 in plain language.
Calculate and interpret the IQR.
Explain percentiles and percentile ranks.
Construct a five-number summary.
Read a boxplot using quartiles and whiskers.
Use 1.5 × IQR fences to flag possible outliers.
Interpret quartiles carefully in context.