Evaluation and review — AQA GCSE Statistics
Test yourself on Evaluation and review with AQA GCSE practice questions.
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Your focus
- Students must understand the importance of evaluating statistical work including:
Evaluation and review exam tips
Quick Revision Summary (Key Takeaway)
Evaluation and review in AQA GCSE Statistics is the final stage of the statistical enquiry cycle, where you judge how reliable, valid and unbiased an investigation is. It involves critiquing sampling methods, data collection, calculations, graphs and conclusions, then suggesting specific improvements to support or challenge statistical claims.
How Students Lose Marks (Examiner Pitfalls)
Pitfall: Students list generic limitations such as 'the sample was small' or 'the question was biased' without linking them to the specific context or explaining the effect on the conclusion.
❌ Weak Answer (Loses Marks):The sample was small so the results are wrong. The question was biased so the data is bad.
Example improved answer:The sample of 30 students from one Year 10 class is a small convenience sample, so it may not represent the 1,200 students in the school. This means the conclusion that 'most students prefer homework on Fridays' may not be valid. A stratified random sample of 100 students across all year groups would improve representativeness.
Examiner Tip: Always name the specific weakness, explain its likely effect on the result or conclusion, and suggest a targeted improvement. Use the context in every sentence.
Pitfall: Confusing reliability with validity, or thinking that repeating a biased survey makes the results valid.
❌ Weak Answer (Loses Marks):The results are reliable because I asked 100 people, so they must be valid.
Example improved answer:Reliability refers to how consistent or repeatable the results are; a large sample may improve reliability, but if the sampling method is biased, the results are not valid. Validity means the data measures what it claims to measure. For example, asking 'Do you enjoy maths?' may not validly measure mathematical ability.
Examiner Tip: Learn the definitions precisely: reliable = consistent, valid = measures the right thing. In evaluation questions, comment on both separately and link to the context.
Step-by-Step Worked Solutions
Question: A local council surveys 40 people leaving a gym between 6pm and 8pm about whether a new leisure centre should be built. 28 say yes. A councillor claims, '70% of residents support the new leisure centre.' Evaluate this claim. (6 marks)
- 1.Step 1: Identify the sample and population: sample = 40 people leaving one gym between 6pm and 8pm; population = all residents in the council area.
- 2.Step 2: Identify sources of bias: gym users are likely to be interested in leisure facilities, so their views may not represent all residents; the time and location exclude non-gym users, shift workers and people who exercise elsewhere.
- 3.Step 3: Calculate the sample proportion: 28 out of 40 = 0.70 = 70%, but this is only the sample percentage, not the population percentage.
- 4.Step 4: Evaluate reliability: a sample size of 40 is small, so another sample could give a very different proportion; the estimate is unreliable.
- 5.Step 5: Evaluate validity: because gym users may be more likely to support a leisure centre, the sample is biased and the claim is not valid for all residents.
- 6.Step 6: Suggest an improvement: use a larger stratified random sample of residents across different age groups, genders and areas, and ask a neutral question.
Final Answer: The claim is not justified: 70% is only the sample proportion from a small, biased sample of gym users. A larger, representative sample is needed before generalising to all residents.
Question: A student records the number of texts sent per day by 20 classmates. The mean is 42 and the median is 35. The student concludes 'The typical number of texts sent by students at the school is 42.' Evaluate this conclusion. (6 marks)
- 1.Step 1: Identify the sample: 20 classmates, likely one class or year group, not the whole school population.
- 2.Step 2: Compare the mean and median: mean = 42 texts, median = 35 texts. The mean is higher than the median, suggesting positive skew or outliers from students who send very many texts.
- 3.Step 3: Consider which average is more representative: the median is less affected by extreme values, so 35 may be a better measure of a typical student in this sample.
- 4.Step 4: Evaluate generalisation: classmates are a convenience sample, so they may not represent all students at the school because of differences in age, phone access and friendship groups.
- 5.Step 5: Evaluate reliability: a sample size of 20 is small, so the mean and median could vary greatly in another sample.
- 6.Step 6: Suggest an improvement: take a larger random or stratified sample across year groups, check for outliers, and report both the mean and median with a measure of spread such as the interquartile range.
Final Answer: The conclusion is not fully supported: 42 is the sample mean, but the median 35 suggests skew, and the sample is small and not representative. A larger random sample and use of the median/IQR would give a more valid conclusion.