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Year 10
Higher

Sampling limitations

I can state the limitations of a sample and the impact of different sample sizes.

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New
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Year 10
Higher

Sampling limitations

I can state the limitations of a sample and the impact of different sample sizes.

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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. A sample can only produce conclusions for that sample.
  2. A different sample may produce different conclusions.
  3. The usefulness of any conclusions may be limited by the sample size.

Keywords

  • Sample - A sample is a subset of the population.

  • Bias - Bias can be present in any sample collected from a population and may affect the results of a statistical investigation.

Common misconception

Samples always represent the population from which they are drawn as they come from that population.

Taking multiple large samples allows us to begin to generalise the results to the whole population.


To help you plan your year 10 maths lesson on: Sampling limitations, download all teaching resources for free and adapt to suit your pupils' needs...

Desmos can be used to simulate rolling a dice if you wish pupils to carry out multiple samples and you do not have access to dice in the classroom.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Capture-recapture is a sampling method which allows you to the size of a population without counting it fully.
Correct Answer: estimate
Q2.
Jacob captures 10 birds and marks each one with some non-toxic dye. Jacob recaptures 10 birds, but finds that none of them have a paper band. Select the possible reasons for this.
Correct answer: Jacob's sample size is too small.
Correct answer: The dye has washed off in the rain.
Jacob might have recaptured the same bird twice.
Q3.
Which of these assumptions are made when the method of capture-recapture is used?
Correct answer: The marked animals have mixed into the population so the recapture is random.
Some of new animals will have been born or migrated into the habitat.
Some of the animals will have migrated or died.
Correct answer: The popluation has remained constant.
Q4.
As part of a capture-recapture sample, 200 fish from a lake are captured and marked with a white dye. During a recapture of 100 fish, 12 were marked with the white dye. Select the correct statement.
$$\frac{x}{200}=\frac{12}{200}$$
$$\frac{100}{200}=\frac{12}{x}$$
$$\frac{100}{200}=\frac{x}{12}$$
Correct answer: $$\frac{200}{x}=\frac{12}{100}$$
$$\frac{200}{x}=\frac{100}{12}$$
Q5.
Laura captures 9 deer and marks them by attaching a tag to their legs. Three days later, Laura recaptures 40 deer, and 4 of them have a tag attached. Estimate the total number of deer.
Correct Answer: 90, 90 deer
Q6.
Jun captures 21 squirrels and marks them by attaching a tag to their legs. Three days later, Jun recaptures 46 squirrels, and 7 of them have a tag attached. Estimate the total number of squirrels.
Correct Answer: 138, 138 squirrels

Exit quiz

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6 Questions

Q1.
__________ can be present in any sample collected from a population and may affect the results of a statistical investigation. 
Correct answer: Bias
Discrete
Randomness
Strata
Q2.
Laura flips a coin three times and it lands heads each time. Laura concludes the coin is biased. Is Laura correct?
Yes, it is definitely biased.
Yes, the chance of 3 heads in a row is very low.
No, Laura needs to flip the coin 3 more times to be sure.
Correct answer: No, Laura needs to flip the coin at least 100 more times.
Q3.
Izzy wants to find out what type of music is most popular among pupils at her school. She asks 5 of her friends who their favourite singer is. Which of these comments are correct?
Correct answer: Izzy has a biased sample as her friends may like the same music.
Correct answer: 5 is too small a sample.
Izzy should ask more pupils from year 10.
Correct answer: Izzy should ask some pupils from each year group.
Izzy should ask some teachers as well.
Q4.
Jacob and Sofia have both investigated what the favourite subject of the year 10 pupils in their school is. sample is more likely to be representative of the population.
An image in a quiz
Correct Answer: Sofia's, Sofia, Sofias
Q5.
Jacob and Sofia have both investigated what the favourite subject of year 10 pupils in their school is. Select the statements that are likely to be true.
An image in a quiz
Correct answer: Jacob should have taken a larger sample.
Jacob had a good sampling method as his sample was more targeted.
Jacob's sample was random.
Sofia should have used a smaller sample.
Correct answer: Sofia's sample was random.
Q6.
Jun wants to find out if the town of Rowanwood needs a new sports centre. Comment on Jun's sampling method.
An image in a quiz
Jun's sample is too big.
Correct answer: Jun's sample will be biased.
Correct answer: Jun shouldn't only ask people at the sports centre
Jun doesn't live in Rowanwood, so shouldn't ask there.
Correct answer: Jun's enthusiasm may influence his results.