AQA A-Level Mathematics: Statistical Sampling: Population and Sample — mark scheme explained

The question

A researcher wants to estimate the average height of students in a school. The school has 1,000 students. Describe how you would use simple random sampling to select a sample of 50 students. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  1. Assign a unique number to each student from 1 to 1,000.

• S2

  2. Use a random number generator or a table of random numbers to select 50 unique numbers between 1 and 1,000.

• S3

  3. Identify the students corresponding to these 50 numbers and include them in your sample.

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   1. Assign a unique number to each student from 1 to 1,000.

2. S2

   2. Use a random number generator or a table of random numbers to select 50 unique numbers between 1 and 1,000.

3. S3

   3. Identify the students corresponding to these 50 numbers and include them in your sample.

4. Final answer: The researcher would assign each student a unique number from 1 to 1,000, use a random number generator to select 50 unique numbers, and then identify the students corresponding to these numbers for the sample.

Common mistakes

• Confusing population and sample — Always clearly define the population as the entire group of interest and the sample as a subset selected for analysis.
• Assuming all samples are representative — Understand that different sampling techniques can lead to different conclusions and consider the context when selecting a sample.
• Using convenience sampling without acknowledging bias — Always acknowledge and discuss the potential biases introduced by opportunity sampling in your analysis.
• Failing to consider sample size — Understand the importance of sample size in reducing sampling variability and improving the reliability of your inferences.
• Not using random number generators for SRS — Use a random number generator or a table of random numbers to ensure that every member of the population has an equal chance of being selected.
• Ignoring sampling variability — Recognize the importance of understanding and accounting for sampling variability in your analysis.
• Failing to critique sampling techniques — Always consider the context and potential biases when selecting a sampling technique and provide a rationale for your choice.

Where the marks go

• Full worked solution (all marking points)3 marks

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