Interpreting and comparing statistical evidence
Read a distribution in context and separate what the data support from claims they cannot establish.
Core and Extended. This is the separate 9–1 qualification 0980. Cambridge intends Core for grades 4–1 and Extended for grades 9–5; the eligible award bands are grades 5–1 for the Core papers and grades 9–3 for the Extended papers.
Before you begin
- Read graph axes and table totals.
- Recognise averages and ranges.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What must be read before comparing bar heights?
What you will learn
- Compare typical values and spread fairly.
- Explain sample, scale and causal limitations.
Compare more than a single headline
Two classes have mean scores 68 and 72. The second has the larger mean, but that alone does not show every student scored better. Their spread and sample sizes also matter: a wide range indicates greater variation, while a small group can be affected strongly by a few extreme scores.
Compare like with like, using the same units, time period and relevant population. Raw counts from groups of different sizes may need percentages. If eight of ten learners and twelve of twenty pass, the first pass rate is 80% and the second 60%, despite the second having more passes.
Check how the evidence was collected and displayed
A graph with a truncated vertical axis can exaggerate differences between bars. Read the actual scale and values rather than judging height alone. Surveying only volunteers or only successful learners may bias a conclusion about all students.
A pattern showing that students who practise more score higher does not by itself prove practice caused the difference. Other factors, such as prior knowledge or support, may contribute. State a conclusion limited to the observed data, and identify a sensible next check rather than inventing certainty.
Pause and explain
8 of 10 pass in A and 12 of 20 in B. Which pass rate is higher?
Worked example
Group A has 8 passes out of 10; Group B has 12 out of 20. Which has the higher pass rate?
Show the worked solution
- A rate is 8/10 = 80%.
- B rate is 12/20 = 60%.
- A has the higher rate even though B has more individual passes.
Answer Group A: 80% versus 60%.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Compare 15 of 25 successes with 18 of 30.
Give me a hint
Calculate each percentage.
Compare my reasoning
- 15/25 = 0.6.
- 18/30 = 0.6.
- Both rates are sixty percent despite different counts.
Both 60%.
Look for these in your work
- Used proportions.
- Avoided comparing counts alone.
Classes have the same mean but ranges 12 and 35. What limited comparison is justified?
Give me a hint
Range describes the span, not the whole shape.
Compare my reasoning
- Their mean scores are equal.
- The range thirty-five class has a wider observed score span.
- This does not alone identify how most scores are clustered or which class is better.
Equal means; wider observed span for range 35.
Look for these in your work
- Compared the stated measures.
- Limited the claim to what range supports.
A study finds an association between coaching use and higher scores. Does it prove coaching caused the higher scores?
Give me a hint
Consider alternative explanations.
Compare my reasoning
- The data show an association.
- Prior ability, motivation or other support may differ.
- A causal claim needs further study that addresses these factors.
No; association alone does not establish causation.
Look for these in your work
- Separated association from cause.
- Named plausible confounding factors.
Common mistakes
- Comparing raw counts across unequal totals.
- Ignoring axis truncation.
- Treating association as proof of cause.
What can you explain now?
Why can a large volunteer sample still be biased?
Compare with the explanation
Volunteers may differ systematically from the whole population.
Sample size does not repair a selection process that excludes relevant groups.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, critique one graph using its scale, sample and the scope of its conclusion.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.