Quartiles, box plots and spread – Year 9 maths lesson
Lesson 20 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why is the IQR a better measure of spread than the range when there is an outlier?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using the range when there is an outlier. The IQR ignores the extremes.
- Comparing only the highest values of two box plots. Compare an average (median) and a spread (IQR).
Tip for home: Compare two sports teams' scores using medians and spreads.
What your child will learn
We are learning to find quartiles and the interquartile range and compare data with box plots.
Success looks like
- I can find quartiles and the IQR.
- I can read a box plot.
- I can compare two sets of data.
Key words
- quartile
- a value that splits ordered data into quarters
- interquartile range
- upper quartile minus lower quartile
- box plot
- a diagram of the five key values
- outlier
- a value far from the rest
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Time how long family members take to do a puzzle and draw a box plot of the times.
The big ideas (for the adult)
Quartiles split ordered data into four equal parts: the lower quartile, the median and the upper quartile.
The interquartile range (IQR) = upper quartile − lower quartile. It measures the spread of the middle half and ignores extreme values.
A box plot shows the minimum, quartiles, median and maximum. To compare two sets, compare the medians and the IQRs.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
GCSE subject content S4: “interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots; appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)”
National Curriculum for England, Year 9: “appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.