Read data with its units, population and limitations
Read scales, totals and units before making comparisons · Relate a conclusion to the original question · Identify limits of the population and collection method
Section E10.1 · Extended · Interpreting statistical evidence
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Fractions and percentages
- Reading tables
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Read scales, totals and units before making comparisons
- Relate a conclusion to the original question
- Identify limits of the population and collection method
What do the numbers describe?
Before interpreting a graph or table, identify the variable, units, population, time period and how data were collected. Read a scale from its tick values: a bar starting at 80 rather than zero can exaggerate a small change. A count alone does not show a rate when groups have different sizes.
Twenty successes among 25 attempts is 80%; thirty among 50 is 60%. The second group has more successes but a lower success rate. State which comparison the original question asks for.
Keep the inference within the evidence
A voluntary survey of website visitors describes its respondents. It need not represent every student, because participation and access may affect who responds. Extended inference should support or question the original conjecture, explain the observed evidence, and acknowledge alternative explanations. An association before and after a change does not by itself isolate the change as its cause.
Sources for this lesson
Pause and explain
Does the larger success count always mean the higher success rate?
Worked example
A claims 20 successes from 25 attempts; B has 30 from 50. Which has the higher success rate?
Show the worked solution
- Calculate 20/25=0.8 and 30/50=0.6.
- Compare rates rather than just success counts.
Answer A has the higher rate, 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.
A has 18 successes from 20 attempts; B has 40 from 50. Compare counts and success rates.
Give me a hint
Use each group’s own total.
Compare my reasoning
- B has more successes: 40 versus 18.
- A has rate 90%, while B has 80%.
B has the larger count; A has the higher rate.
Look for these in your work
- Use matching denominators
- Answer both comparisons
A chart shows values 82 and 84 with its vertical scale starting at 80. Find the actual increase and its percentage relative to 82.
Give me a hint
Use the values rather than the apparent bar-height ratio.
Compare my reasoning
- The increase is 2 units.
- Percentage increase is (2/82)×100≈2.44%.
2 units, approximately 2.44%; the value has not doubled.
Look for these in your work
- Read the axis origin
- Choose the correct percentage base
Seventy of 100 voluntary website respondents prefer evening study. Can a report conclude that 70% of all students prefer evenings? Explain.
Give me a hint
Check the sampled population and selection method.
Compare my reasoning
- The observed proportion is 70% of respondents.
- Voluntary website participation may differ from the whole student population.
No; 70% describes these respondents, with wider inference limited by selection and coverage.
Look for these in your work
- Name the observed group
- Limit the claim to the evidence
Common mistakes
- Check a truncated axis before judging visual differences.
- A respondent group is not automatically a representative population sample.
What can you explain now?
Does the larger success count always mean the higher success rate?
Compare with the explanation
No; divide by the corresponding number of attempts.
Groups with different denominators can reverse the count comparison.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Does the larger success count always mean the higher success rate?
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.