Sampling
Probability and statistics
- Foundation
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Explain what a sample is.
2 marks
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A school has $800$ students and a sample of $50$ is taken. What is the population?
2 marks
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Give one advantage and one disadvantage of using a sample.
3 marks
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Describe a random sample of the students, including a method for choosing it.
3 marks
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A club has $120$ members: $72$ adults and $48$ children. A stratified sample of $20$ is needed. How many adults and how many children should be included?
4 marks
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A factory makes $500$ items a day and tests a sample of $40$. Give a reason for not testing every item, and write the sample as a fraction of the daily production.
4 marks
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Year groups have $150$, $120$, $180$ and $150$ students. A stratified sample of $40$ is taken. How many students should be chosen from each year?
5 marks
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A council wants opinions on a park. Explain why asking only people in the park on Saturday morning may be biased. The town has $5000$ adults and $2000$ children, and a stratified sample of $70$ is planned. How many of each are needed? Suggest how to choose the adults, and give one reason for and against using a larger sample.
6 marks
Mark scheme
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Answer. A sample is part of a population, chosen so that you can find out about the whole population.
- It is a subset of the population.
- It is used to draw a conclusion about the population.
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Answer. The $800$ students
- The population is the whole group being studied.
- $800$ students
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Answer. A sample is quicker or cheaper. It may not represent the population.
- Advantage: less time or cost than asking everyone.
- Disadvantage: the sample can be biased or unrepresentative.
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Answer. Every student has an equal chance. Number the students and use a random number generator.
- A random sample gives each member an equal chance of selection.
- A random number generator, or drawing numbers from a hat, can choose them.
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Answer. $12$ adults and $8$ children
- Adults: $\dfrac{72}{120} \times 20 = 12$.
- Children: $\dfrac{48}{120} \times 20 = 8$.
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Answer. Testing all of them may be too slow, or the test may damage the items. The sample is $\dfrac{2}{25}$.
- A reason such as time, cost or a destructive test.
- $\dfrac{40}{500} = \dfrac{2}{25}$
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Answer. $10, 8, 12$ and $10$
- The total is $600$.
- $\dfrac{150}{600} \times 40 = 10$, $\dfrac{120}{600} \times 40 = 8$, $\dfrac{180}{600} \times 40 = 12$ and the last year also gives $10$.
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Answer. People already in the park are more likely to be users. Choose $50$ adults and $20$ children. A larger sample can be more reliable, but it costs more time.
- Saturday-morning park users are not a random cross-section of the town.
- Adults: $\dfrac{5000}{7000} \times 70 = 50$. Children: $20$.
- Number the adults and use a random number generator.
- A larger sample usually represents the town better, but it takes more time and money.