Box plots and interquartile range – Grade 7 math lesson
Lesson 20 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 7 (ages 12–13)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Sampling and making inferences
Curriculum
Common Core State Standards 7.SP.B.3: “Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.”
Common Core State Standards 7.SP.B.4: “Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.