The Five-Number Summary
📦 The Five-Number Summary
Imagine you're comparing the performance of two basketball teams and need to quickly see which has more consistent scoring. A box plot is like a visual summary that shows you the "box of performance" - where the middle 50% of scores lie, plus the whiskers that extend to show the full range. With just one glance, you can see which team is more consistent, which has higher typical scores, and whether there are any unusual outliers that might skew your analysis.
Mathematics glossary
- What is a box plot?
- A box plot (or box-and-whisker diagram) is a visual display of the five-number summary of a dataset: minimum, Q1, median, Q3, and maximum. It shows the distribution and spread of data in a compact form.
- What is the five-number summary?
- The five-number summary consists of: 1. Minimum (smallest value) 2. Q1 (lower quartile) 3. Median (middle value) 4. Q3 (upper quartile) 5. Maximum (largest value)
Earn the mark scheme marks
💡 Exam Tips for Box Plots
Drawing Box Plots:
- Use a ruler: Draw neat, straight lines
- Equal scale: Use consistent spacing on your number line
- Clear markers: Mark all five values clearly
- Proper proportions: Box and whisker lengths should reflect actual data
- Vertical alignment: Keep everything at the same height
Finding Quartiles:
- Even n: Split data exactly in half, find medians of each half
- Odd n: Exclude the overall median, find medians of each half
- Double-check: Q1 < Median < Q3 always
- Calculator method: Learn your calculator's quartile functions
Interpretation:
- Compare medians: For typical values
- Compare IQRs: For consistency
- Look at skewness: Position of median in box
- Consider context: What do the numbers represent?
Now try it yourself
Quiz · Question 1 of 18
On a box plot, what does the box (the rectangle) represent?
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on box plots, with a full worked answer.
AQA Paper 3
Two of the four sittings we have full papers for give summary statistics and ask for a full box plot to be constructed from them.
Edexcel Paper 2
Two of the three sittings we have full papers for give a named person's specific, wrong mathematical statement and ask for an explanation of why it is incorrect.