Medium2 marksStructured
AQA GCSE · Question 17.4 · Data Collection and Sampling Methods
Tom reads that HS2 will link 29 stations. He decides to take a random sample of 5 of the stations where he can ask people for their opinions. Briefly describe a way Tom could achieve this.
Tom reads that HS2 will link 29 stations. He decides to take a random sample of 5 of the stations where he can ask people for their opinions. Briefly describe a way Tom could achieve this.
How to approach this question
To create a simple random sample, every item in the population (all 29 stations) must have an equal chance of being selected. Describe a step-by-step process for this.
1. How would you represent all the stations? (e.g., a list, names in a hat).
2. How would you make the selection random? (e.g., random number generator, pulling from a hat).
3. How many would you select?
Full Answer
1. Assign a number to each of the 29 stations, from 1 to 29.
2. Use a random number generator (or pull numbers from a hat) to select 5 unique numbers between 1 and 29.
3. The 5 stations corresponding to these numbers will form the random sample.
A simple random sample ensures that every possible sample of size 5 has an equal chance of being selected. A practical way for Tom to do this is:
1. **Create a sampling frame:** Make a list of all 29 HS2 stations and assign a unique number to each one, from 1 to 29.
2. **Random Selection:** Use a random method to select 5 numbers. For example:
- Write each number from 1 to 29 on identical pieces of paper, put them in a hat, mix them thoroughly, and draw out 5 pieces of paper.
- Or, use a random number generator on a calculator or computer to generate 5 unique random integers between 1 and 29.
3. **Identify the Sample:** The 5 stations that correspond to the selected numbers become the sample for his study.
Common mistakes
✗ Describing a non-random method like "pick the 5 biggest stations" or "pick the 5 closest stations".\n✗ Being too vague, e.g., "pick 5 at random" without describing *how*.
Practice the full AQA GCSE Statistics Foundation Tier Paper 2
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