GCSE MATHS • HIGHER TIER
Comparing Box Plots Made Simple
Learn how to compare medians, interquartile ranges and ranges, judge consistency, and write strong GCSE comparison statements using numerical evidence.
Clear method
Exam practice
Worked proofs
Three-Figure Bearings in Four Moves
1
Read
Read the five key value: minimum, lower quartile, median, upper quartile and maximum.
2
Compare
Compare the medians to discuss the typical values of the datasets.
3
Measure Spread
Compare the interquartile ranges and overall ranges to describe spread and consistency.
4
Support
Use numerical evidence from the box plots to support every comparison.
What You’ll Learn
Understand Box Plots
Recognise how a box plot summarises a dataset using the minimum, lower quartile, median, upper quartile and maximum.
Compare Typical Values
Use the median to decide which dataset has the higher or lower typical value.
Compare Consistency
Use the interquartile range to compare the spread of the middle 50% of each dataset.
Compare Overall Spread
Use the range to compare variation across the whole dataset.
Write Strong Comparisons
Make comparison statements that include numerical evidence and explain what the values mean.
Key Rules
Median
A higher median generally means a higher typical value.
Interquartile Range
IQR = Q3 - Q1
Range
Range = Maximum - Minimum
Use Evidence
State the relevant values when comparing two box plots rather than making vague statements.
More Worked Examples
1
Comparing IQR
Data Set A: Q1 = 20, Q3 = 40
IQR = 40 - 20 = 20
Data Set B: Q1 = 15, Q3 = 50
IQR = 50 - 15 = 35
Data Set B: Q1 = 15, Q3 = 50
IQR = 50 - 15 = 35
2
Comparing Range
Data Set A: Minimum = 10, Maximum = 60
Range = 60 - 10 = 50
Data Set B: Minimum = 15, Maximum = 55
Range = 55 - 15 = 40
Data Set B: Minimum = 15, Maximum = 55
Range = 55 - 15 = 40
3
Comparing Medians
Data Set A median = 38
Data Set B median = 45
4
Comparing Consistency
Data Set A IQR = 18
Data Set B IQR = 25
- Common GCSE Mistakes
- Wrong measure: Do not use range when the question is asking about consistency.
- IQR error: Calculate Q3 - Q1 carefully.
- Vague comparison: Support statements with numerical evidence.
- No interpretation: Explain what the median, IQR or range shows.
- Exam Tips
- Compare medians: Use them to discuss typical values.
- Compare IQRs: Use them to discuss consistency.
- Compare ranges: Use them to discuss overall spread.
- Quote numbers: Include values from both datasets.
- Explain meaning: Say what the comparison tells you about the data.
Skills Used in Comparing Box Plots
Cumulative Frequency Graphs
Median and Quartiles from Graphs
Drawing Box Plots
Interquartile Range
Histograms
Statistics and Data Handling
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Comparing Box Plots Tutorial
Step-by-step walkthroughs of Comparing Box Plots with clear methods and exam tips.
Frequently Asked Questions
A box plot is a graph that summarises data using the minimum, lower quartile, median, upper quartile and maximum.
The median represents the middle value and is used to compare typical values between datasets.
The IQR shows the spread of the middle 50% of the data and is useful for comparing consistency.
Add 180° if the bearing is below 180°, or subtract 180° if it is above 180°.
Compare relevant measures, include numerical evidence from both datasets and explain what the values show.
