Statistics & Probability · Topic 3 of 4
Interpreting Graphs & Tables
Theory
This skill is about reading data that is given to you — in graphs and tables — and using it to answer questions and make decisions. It is the reverse of the “Statistical Diagrams” topic, which is about constructing them.
1. Reading a Graph
Before extracting anything, check four things: the title/text (what the graph is about), the scale on each axis, the key (for compound or comparative charts), and the overall trend. Typical questions ask you to:
- state a specific total, or the most / least popular option;
- express a value as a fraction or percentage of the total;
- scale a total up (e.g. from one hour to a whole day or week);
- make a fair comparison and choose the best or worst option.
2. Reading a Table
Tables (price lists, timetables, tax bands, exchange rates) pack a lot of information into rows and columns. Find the correct cell, combine the values the question needs, and watch for conditions written in the small print (e.g. “a stay crossing into a second month is charged at the higher rate”).
3. Justifying a Decision
Applications questions often ask you to choose the better option and justify it with the numbers. A choice without a supporting calculation earns no marks — always show the comparison.
The Golden Rule: compare like for like. If one figure is a percentage, convert the others to percentages too; if amounts cover different time periods or group sizes, put them on the same footing before you compare. And read the scale and key first — two graphs drawn the same size can use very different scales.
⚠️ Common Examiner Traps
- Different scales: when comparing two graphs, a taller bar does not always mean a bigger value — check the axis scale on each.
- Raw number vs proportion: “most visitors” and “highest proportion of visitors” are different questions — decide which is being asked.
- Table small print: a condition hidden in the text (a surcharge, a minimum, a different rate) is usually the key to the marks.
- Justify with numbers: stating which option is better without the calculation to back it up scores nothing.
Worked examples
Example 1
Reading a Comparative Chart
A shopping centre recorded, over one hour, how many people entered each of three cafés and how many of them bought a hot drink:
- Café A: 60 visitors, 45 bought a hot drink
- Café B: 50 visitors, 20 bought a hot drink
- Café C: 40 visitors, 26 bought a hot drink
(a) Which café was busiest? (b) Café C claims it had the highest proportion of visitors buying a hot drink. Is this correct? (c) If Café A keeps this rate over a 10-hour day, how many visitors would it expect?
(a) Busiest means the most visitors: Café A, with 60.
(b) “Proportion” means compare like for like as percentages:
Café A has the highest proportion (75%), so Café C's claim is incorrect.
(c) Scale the one-hour figure up: visitors.
Example 2
Reading a Price Table
A campsite charges the following per night (£). Each extra adult beyond those included costs £8 per night.
- Low season — Tent £18, Caravan £30, Lodge £55
- High season — Tent £26, Caravan £42, Lodge £78
(a) What is the cost of a caravan for 4 nights in low season? (b) A group books a lodge for 3 nights in high season, with 1 extra adult. What is the total cost?
(a) Read the low-season caravan rate (£30) and multiply by the nights:
(b) Lodge at the high-season rate for 3 nights, plus the extra adult at £8 per night:
Example 3
🎯 Exam-style (justify a decision)
A customer wants to join a gym for 8 months. FitZone charges a £25 joining fee plus £20 per month. FlexFit has no joining fee but charges £24 per month. Which gym is cheaper over the 8 months, and by how much? Justify your answer.
Step 1: Work out the full cost of each — do not compare the monthly rates alone, because of the joining fee.
Step 2: Compare and state the difference:
Answer: FitZone is cheaper, by over the 8 months.