Read directly
What value, category or frequency is shown? Does the vertical axis start at zero? Are class intervals equal?
CAMBRIDGE O LEVEL · 2025–2027
Interpreting statistical data.
Read the evidence, compare typical values and spread, and explain the limits of a conclusion.
BY THE END
Interpret tables and graphs · compare averages and spread · recognise restrictions on inferences
01
Read the context, scale and population
A graph is evidence about a particular collection, not a universal statement. Before interpreting it, find out who or what was measured, what the units mean and how the observations were obtained.
Read the scale and key before judging the picture. Bar height, area, counts and percentages do not always represent the same thing. Separate a direct reading, such as a frequency, from an inference, such as a claim about a wider population.
Start with the title, units, axes, key and the group represented. Distinguish a frequency from a percentage, and an observation from an estimate.
Infer carefully
What pattern does the evidence support? How large and representative is the sample? Could a different explanation fit?
WORKED EXAMPLE
12 of 30 students in one class walk to school. Can we say 40% of the whole school walk?
1230 = 40% of this class. The whole-school claim requires evidence that the class represents the school. One class alone may give a misleading estimate.
Pause and explainWhy read the vertical-axis labels before comparing bar heights?
A truncated or unusual scale can exaggerate or alter the visual impression. The labelled values give the actual comparison.
02
Compare a typical value and the spread
An average compresses a data set into a typical value, but it hides how widely the individual observations vary. Two groups can share a mean while one contains much more extreme results.
Compare a measure of centre and a measure of spread, giving their numbers and meanings in context. Then check whether an extreme observation influences the comparison. A higher value is not always better: higher test scores and higher waiting times have different interpretations.
| Group | Scores | Mean | Median | Range |
|---|---|---|---|---|
| A | 4, 5, 5, 6, 10 | 6 | 5 | 6 |
| B | 5, 6, 6, 6, 7 | 6 | 6 | 2 |
WORKED EXAMPLE
Compare the performance and consistency of groups A and B.
The groups have the same mean score, 6. Group B has a higher median, 6 compared with 5, and a smaller range, 2 compared with 6. B’s scores are more consistent by this measure.
A’s score of 10 raises its mean above its median. Give the numerical comparison and explain it in context.
Pause and explainWhat does a smaller range suggest about otherwise comparable delivery times?
They are more consistent by that measure, with a smaller gap between the fastest and slowest delivery.
03
Match the conclusion to the evidence
A conclusion can be numerically correct for a sample and still be unjustified for everyone else. The strength of the claim must match the amount and quality of the evidence.
Ask whether the sample represents the target population, whether group sizes differ, and whether another factor could explain a relationship. Comparing percentages can correct unequal totals, but it does not by itself remove sampling bias or establish causation.
| Issue | What to say |
|---|---|
| Small or unrepresentative sample | The pattern may not apply to the whole population. |
| Different sample sizes | Compare proportions or percentages when counts alone are misleading. |
| Truncated axis or unequal scales | Check actual values rather than judging bar heights alone. |
| Correlation | An association does not establish cause and effect. |
| Outside the observed range | An extrapolated prediction may be unreliable. |
WORKED EXAMPLE
Club A has 18 passes out of 20 tests; Club B has 24 out of 30. Which has the higher pass rate?
A: 1820 × 100% = 90%
B: 2430 × 100% = 80%
B: 2430 × 100% = 80%
B has more passes, but A has the higher pass rate. Neither result alone proves one teaching method caused better performance.
Pause and explainDoes a larger sample automatically remove bias?
No. A large sample chosen from an unrepresentative group can still give a misleading population estimate.
04
Your turn. Support each conclusion.
Give a number to support each comparison and name the relevant group or measurement. Avoid saying one group is “better” without explaining the context.
Finish by checking whether the conclusion applies only to the observed sample or is supported for a wider population. State a concrete restriction rather than a vague warning that the data might be wrong.
1
Two groups have medians 14 and 18, and ranges 9 and 4. Compare them.
Reveal worked answer
The second group has a higher median (18 versus 14) and less spread by range (4 versus 9). Whether higher is preferable depends on the context.
2
A survey of 10 members of a sports club finds that 9 exercise daily. Give a restriction on a town-wide conclusion.
Reveal worked answer
Sports-club members may not represent the town, and the sample is small. We can state 90% for this sample, but not assume the same for the town.
3
One group has 15 successes in 25 attempts; another has 21 in 30. Compare success rates.
Reveal worked answer
1525 = 60%; 2130 = 70%. The second group has the higher success rate.
4
A graph shows that students who revise more tend to score more. Does this prove revision time alone determines the score?
Reveal worked answer
No. This is an association; other factors can affect scores. Correlation alone does not establish causation.