ExpertHard7 marksExtended Response
AQA GCSE · Question 06.3 · Data Collection and Sampling Methods
Tom wants a sample of Year 7 students and a sample of Year 11 students to complete a questionnaire for him. He considers these three sampling methods for Year 7 students.
Method A
Number all the students in Year 7. Obtain 30 random numbers. Ask the students whose random numbers come up to complete the questionnaire.
Method B
Wait outside the dinner hall. Ask the first 30 Year 7 students he sees to complete the questionnaire.
Method C
Choose three Year 7 students from each of the 10 maths sets. Ask these students to complete his questionnaire.
Name and compare the merits of each sampling method. Make a reasoned choice of which method Tom should use.
Tom wants a sample of Year 7 students and a sample of Year 11 students to complete a questionnaire for him. He considers these three sampling methods for Year 7 students.
Method A
Number all the students in Year 7. Obtain 30 random numbers. Ask the students whose random numbers come up to complete the questionnaire.
Method B
Wait outside the dinner hall. Ask the first 30 Year 7 students he sees to complete the questionnaire.
Method C
Choose three Year 7 students from each of the 10 maths sets. Ask these students to complete his questionnaire.
Name and compare the merits of each sampling method. Make a reasoned choice of which method Tom should use.
How to approach this question
1. **Identify and Name Each Method**:
* Method A: Every student is numbered, and random numbers are used. This is **Simple Random Sampling**.
* Method B: "Ask the first 30..." This is **Convenience Sampling** (or Opportunity Sampling).
* Method C: The population (Year 7) is divided into groups (maths sets), and a sample is taken from each group. This is **Stratified Sampling**.
2. **Analyse Merits (Pros) and Demerits (Cons) for Each**:
* **Method A**: Pro - Unbiased, representative. Con - Can be time-consuming.
* **Method B**: Pro - Quick, easy. Con - High risk of bias, unrepresentative.
* **Method C**: Pro - Ensures all sub-groups (maths sets) are included. Con - May not be proportional if sets are different sizes.
3. **Compare the Methods**: Directly compare their strengths and weaknesses. State that Method B is the worst due to bias. Compare A and C in terms of bias and representativeness.
4. **Make a Reasoned Choice**: Choose one method (A or C are the best choices) and justify why it is better than the others. For example, choose A because it is the simplest unbiased method. Or, choose C because it guarantees representation of all ability levels, but acknowledge the potential issue with set sizes.
Full Answer
**Method A: Simple Random Sampling**
* **Merits**: This method is unbiased as every student in Year 7 has an equal chance of being selected. It is likely to produce a representative sample of the Year 7 population.
* **Demerits**: It can be time-consuming to get a list of all students and their corresponding numbers.
**Method B: Convenience Sampling**
* **Merits**: This method is quick and easy to carry out.
* **Demerits**: It is highly likely to be biased. The first 30 students seen might all be from one friendship group or one class, making the sample unrepresentative of the whole year group.
**Method C: Stratified Sampling**
* **Merits**: This method ensures that all maths sets (strata) are represented in the sample, in this case equally. This can make the sample more representative of the range of abilities across the year group.
* **Demerits**: It assumes that the maths sets are of equal size. If they are not, taking three from each set would lead to a disproportionate sample. It can also be complex to organise.
**Comparison and Choice**
Method B is the weakest as it is a convenience sample and very likely to be biased.
Method A (Simple Random) is good because it is unbiased.
Method C (Stratified) is also good as it ensures representation from all ability groups.
**Reasoned Choice**
Tom should use **Method A (Simple Random Sampling)**. Although Method C is also strong, we don't know if the maths sets are of equal size. Simple random sampling is the most straightforward way to get an unbiased sample where every individual has an equal chance of selection, which is the gold standard for avoiding bias. If the maths sets were of different sizes, a proportional stratified sample would be better, but Method A avoids this complication and is robustly unbiased.
This question requires an evaluation of three different sampling methods.
* **Method A is Simple Random Sampling.** Its main advantage is that it is free from bias, as every student has an equal chance of being selected. This makes it likely to be representative. A disadvantage is the practical effort of numbering everyone and generating random numbers.
* **Method B is Convenience Sampling.** Its only advantage is that it is quick and easy. However, it is a non-random method and is highly susceptible to bias. The sample is unlikely to be representative of the entire year group.
* **Method C is Stratified Sampling.** The population is divided into strata (maths sets). The advantage is that it guarantees representation from all strata (in this case, all ability levels). A potential disadvantage is that it is not a proportional sample; it takes 3 students from each set regardless of the set's size. If Set 1 has 30 students and Set 10 has 15, this method would over-represent Set 10.
**Conclusion:** Method B is the worst choice due to the high risk of bias. Between A and C, Method A is a very strong choice as it is purely random and unbiased. Method C is also strong but has a potential flaw if the set sizes are unequal. A good conclusion would be to recommend Method A as the most reliable way to get an unbiased sample without making assumptions about the sizes of the maths sets.
Common mistakes
✗ Not using the correct statistical names for the methods.
✗ Only listing advantages or disadvantages, not both.
✗ Making a choice without a clear justification that compares it to the other methods.
✗ Stating that Method C is a quota sample. It is stratified because the strata (maths sets) are pre-defined groups.
Practice the full AQA GCSE Statistics Higher Tier Paper 1
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