Box plots and interquartile range – Grade 11 math lesson
Lesson 21 of 23 in the Grade 11 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
- 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 11 math lessons
- Complex numbers
- Radicals
- Vectors
- Laws of exponents
- Square roots and cube roots
- Systems of equations
- Rational expressions and polynomials
- Arithmetic and geometric sequences
- Iteration
- Functions
- Graphing functions
- Exponential functions
- Trigonometric functions
- Law of sines and law of cosines
- Coordinate geometry
- Counting outcomes
- Experimental probability
- Compound events
- Conditional probability
- Expected value
- Scatter plots and lines of fit
- Sampling and making inferences
Curriculum
Common Core State Standards HSS.ID.A.3: “Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).”
Common Core State Standards HSS.ID.A.4: “Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.