Sampling and Bias worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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2 marks
Zainab wants to find out how healthily people eat in she town.
She asks the first 30 people she sees in the queue at a burger van.
(a)Explain why Zainab's sample is likely to be biased.
(b)Describe one way she could improve the way the sample is chosen.
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3 marks
There are \(1200\) students in a large school. Two people each take a random sample to find out how many of them walk to school.
Rosa asks \(20\) students. \(13\) of them say they do.
Callum asks \(80\) students. \(26\) of them say they do.
(a)Use Callum's sample to estimate how many of the \(1200\) students walk to school.
(b)Whose estimate is likely to be the more reliable?
Explain your answer.
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3 marks
A school has \(500\) pupils. A sample of \(25\) pupils is needed.
Three people each describe a different way of choosing the sample.
State the name of the sampling method each one is describing.
(a)Ayesha splits everybody into age groups and then takes a number from each group in proportion to the size of that group.
(b)Daniel numbers everybody in the population and then uses a random number generator to decide who is in the sample.
(c)Freya puts everybody in a list and then takes one at equal intervals all the way down it.
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3 marks
A bottling plant makes \(1250\) bottles in a day.
Owen checks the quality of a systematic sample of \(50\) bottles, taken evenly through the day's production.
(a)Work out how often he should take a bottle, so that the \(50\) bottles are spread evenly through the \(1250\).
(b)Owen says the 50 bottles are a random sample.
Explain why he is wrong.
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3 marks
There are \(1200\) students at Anya's school.
She asks a random sample of \(80\) of them whether they walk to school. \(21\) of them say they do.
(a)Use her sample to estimate how many students at the school walk to school.
(b)Explain why this is only an estimate.
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4 marks
Mr Doyle is taking a stratified sample of \(38\) students from the \(950\) students in his school.
The table shows how many students are in each year group.
Year group 9 10 11 Total Number of students 375 350 225 950 (a)Calculate how many Year \(10\) students should be in the sample.
(b)Calculate how many Year \(11\) students should be in the sample.
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2 marks
Rosa wants to find out how people travel to work in she town.
She asks the first 60 people she sees at a bus stop.
(a)Explain why Rosa's sample is likely to be biased.
(b)Describe one way she could improve the way the sample is chosen.
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3 marks
There are \(800\) students in a large school. Two people each take a random sample to find out how many of them walk to school.
Sian asks \(25\) students. \(8\) of them say they do.
Jonah asks \(80\) students. \(23\) of them say they do.
(a)Use Jonah's sample to estimate how many of the \(800\) students walk to school.
(b)Whose estimate is likely to be the more reliable?
Give a reason for your answer.
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3 marks
A sports club has \(500\) members. A sample of \(50\) members is needed.
Three people each describe a different way of choosing the sample.
Write down the name of the sampling method each one is describing.
(a)Ayesha puts everybody in a list and then takes one at equal intervals all the way down it.
(b)Daniel splits everybody into age groups and then takes a number from each group in proportion to the size of that group.
(c)Freya numbers everybody in the population and then uses a random number generator to decide who is in the sample.
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3 marks
A bottling plant makes \(450\) bottles in a day.
Rosa checks the quality of a systematic sample of \(30\) bottles, taken evenly through the day's production.
(a)Work out how often she should take a bottle, so that the \(30\) bottles are spread evenly through the \(450\).
(b)Rosa says the 30 bottles are a random sample.
Explain why she is wrong.
Answers
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(a) People queuing at a burger van are not typical of everyone in the town, and they were all asked in one place at one time.
(b) Choose people at random from a list of everyone in the town, and ask them at several different times and places. -
(a) \(390\)
(b) Callum, because a larger sample is more likely to be typical of the population, so chance variation has less effect on the estimate. -
(a) Stratified sampling
(b) Random sampling (a simple random sample)
(c) Systematic sampling -
(a) every 25th bottle
(b) Once the first bottle has been chosen, every other bottle in the sample is fixed, so not every group of 50 bottles is equally likely to be chosen. -
(a) \(315\)
(b) It is worked out from a sample, not from the whole school, so a different sample of 80 students would have given a different answer. -
(a) \(14\)
(b) \(9\) -
(a) People standing at a bus stop are far more likely to travel by bus than people in general.
(b) Choose people at random from a list of everyone in the town rather than from one bus stop. -
(a) \(230\)
(b) Jonah, because a larger sample is more likely to be typical of the population, so chance variation has less effect on the estimate. -
(a) Systematic sampling
(b) Stratified sampling
(c) Random sampling (a simple random sample) -
(a) every 15th bottle
(b) Once the first bottle has been chosen, every other bottle in the sample is fixed, so not every group of 30 bottles is equally likely to be chosen.