Statistics
Grade 6-7Box Plots
A box plot summarises a whole data set using just five values, the minimum, lower quartile, median, upper quartile and maximum, making it easy to compare the average and spread of two distributions at a glance. This lesson covers reading these values from a box plot, finding the range and interquartile range, drawing a box plot from a five-number summary, and comparing two distributions.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Reading the five key values
The ends of the whiskers show the minimum and maximum values, the ends of the box show the lower and upper quartiles, and the line inside the box shows the median.
A box plot shows the time taken by 40 students to complete a puzzle. The line inside the box is at 27, so the median time is 27 minutes.
Finding the range and interquartile range
The range is the maximum minus the minimum, found from the ends of the whiskers. The interquartile range is the upper quartile minus the lower quartile, found from the ends of the box.
With a minimum of 8, maximum of 46, lower quartile of 18 and upper quartile of 36, the range is 46 − 8 = 38 minutes, and the interquartile range is 36 − 18 = 18 minutes.
Drawing a box plot
Plot the minimum and maximum as the ends of the whiskers, plot the lower and upper quartiles as the ends of the box, and draw a line inside the box at the median.
For a data set with minimum 8, lower quartile 18, median 27, upper quartile 36 and maximum 46, draw the box from 18 to 36 with a line at 27, and whiskers extending to 8 and 46.
Comparing two distributions
Compare the medians to say which data set is generally higher or lower, and compare the interquartile ranges to say which data set is more or less spread out, or consistent.
Before training, the median time was 27 minutes with an interquartile range of 18. After training, the median fell to 19 minutes with an interquartile range of 15, so students were generally faster and more consistent after training.
Worked Examples
Three exam-style questions, fully solved.
The box plot shows the time taken by 40 students to complete a puzzle, with the median line at 27. Write down the median time.
Easy- 1.Read the value where the line inside the box is drawn: 27
Answer: 27 minutes
The box plot shows the time taken by 40 students to complete a puzzle, with minimum 8, lower quartile 18, upper quartile 36 and maximum 46. Find the range and the interquartile range.
Medium- 1.Find the range using the minimum and maximum: 46 − 8 = 38 minutes
- 2.Find the interquartile range using the quartiles: 36 − 18 = 18 minutes
Answer: Range = 38 minutes, interquartile range = 18 minutes
The box plots show the time taken by the same 40 students to complete a puzzle, before and after a training session. Before training, the median was 27 minutes with an interquartile range of 18. After training, the median was 19 minutes with an interquartile range of 15. Compare the two distributions.
Hard- 1.Compare the medians: the median decreased from 27 to 19 minutes
- 2.Compare the interquartile ranges: the interquartile range decreased from 18 to 15 minutes
Answer: Students were generally faster and more consistent after training
Avoid These
The most common mistakes students make.
Confusing the median line inside the box with one of the quartiles, especially when it is not positioned centrally within the box.
Mistaking the whiskers for the quartiles, when the whiskers actually show the minimum and maximum values.
Using the quartiles instead of the minimum and maximum when finding the range, or using the minimum and maximum instead of the quartiles when finding the interquartile range.
When comparing two box plots, only comparing the medians or only comparing the spread, instead of commenting on both the average and the consistency of the data.
Forgetting that each quarter of the data represents 25% of the total when estimating how many values lie beyond a quartile.
FAQ
Questions parents and students ask.
Before this topic, make sure you know
What to learn next
Want a plan built around your child specifically?
Get our free 8-video course, or book a free Roadmap Call for a personalised plan.