GCSE MATHS • HIGHER TIER
Drawing Box Plots Made Simple
Learn how to use the five-number summary to draw box plots accurately, calculate range and interquartile range, and compare distributions.
Clear method
Exam practice
Worked proofs
Drawing Box Plots in Four Moves
1
Find
Find the minimum, lower quartile, median, upper quartile and maximum.
2
Scale
Draw a suitable horizontal scale that includes all five values.
3
Plot
Mark the five values accurately on the scale.
4
Draw
Draw the box from Q1 to Q3, add the median line and extend whiskers to the minimum and maximum.
What You’ll Learn
Understand Box Plots
Understand how a box plot summarises a dataset using five key values.
Use the Five-Number Summary
Identify the minimum, Q1, median, Q3 and maximum.
Draw Box Plots
Plot the five values accurately and construct the box and whiskers.
Interpret and Compare Data
Use medians, ranges and interquartile ranges to describe and compare distributions.
Key Rules
Five-number summary
Minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum.
Range
Range = Maximum - Minimum
Interquartile range
IQR = Q3 - Q1.
The box
The box runs from Q1 to Q3 and represents the middle 50% of the data.
The whiskers
Whiskers extend from the box to the minimum and maximum values.
Worked Proof: Box Plot
How to Draw a Box Plot
- 1. Find the minimum value.
- 2. Find the lower quartile (Q1).
- 3. Find the median.
- 4. Find the upper quartile (Q3).
- 5. Find the maximum value.
- 6. Draw a horizontal scale.
- 7. Mark the five values.
- 8. Draw a box between Q1 and Q3.
- 9. Draw a line at the median.
- 10. Draw whiskers from the box to the minimum and maximum values.
More Worked Examples
1
Finding the Range
Question: Find the range.
Minimum = 12
Maximum = 45
Range = 45 - 12 = 33
Maximum = 45
Range = 45 - 12 = 33
- Explanation: The range measures the overall spread of the data.
2
Bearing of West
Question: What is the bearing of West?
North to West clockwise is 270°.
- Explanation: The IQR measures the spread of the middle 50% of the data.
3
Angle Less Than 100°
Question: A direction is 45° clockwise from North. Write the bearing.
Use a leading zero because the angle is less than 100°.
- Explanation: A smaller IQR indicates greater consistency.
4
Three-Figure Angle
Question: A direction is 120° clockwise from North. Write the bearing.
The angle is already written using three figures.
- Answer: Data Set A has the higher typical value.
- Common GCSE Mistakes
- Range vs IQR: Do not confuse overall spread with the middle 50%.
- Quartile positions: Plot Q1 and Q3 accurately on the scale.
- Box meaning: Remember the box represents the middle 50% of the data.
- Vague comparisons: Support comparisons with actual numerical values.
- Exam Tips
- Check the scale: Use equal intervals and include all five values.
- Label carefully: Plot each summary value in the correct position.
- Use evidence: Quote medians, ranges or IQRs when comparing.
- Check whiskers: Extend them to the minimum and maximum values.
- Know the measures: Range and IQR describe different types of spread.
Topics to Revise Next
Cumulative Frequency Graphs
Median and Quartiles from Graphs
Interquartile Range
Histograms
Statistics
Data Handling
Ready to Practise?
Printable Worksheet
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Interactive Quiz
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Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Drawing Box Plots Tutorial
Step-by-step walkthroughs of Drawing Box Plots with clear methods and exam tips.
Frequently Asked Questions
A box plot is a graphical summary of data using the minimum, Q1, median, Q3 and maximum.
Minimum, lower quartile, median, upper quartile and maximum.
Subtract the minimum value from the maximum value.
Subtract Q1 from Q3.
