Sampling and Bias Worksheet with Answers

Sampling and Bias

discia.org 10 questions · 32 marks

Name Date

Either paper 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.

Show answer

(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.

Another like this
Either paper 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.

Show answer

(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.

Another like this
Either paper 1 mark

Callum's school has Years 7 to 11.

Callum claims that most of the pupils in his school walk to school.

Callum asks 80 pupils from Years 7 to 9.

Give a reason why this sample may not be useful in testing Callum's claim.

Show answer

The sample leaves out Years 10 and 11. Pupils in those years may differ in how they travel to school, so the sample may not represent all the pupils.

Another like this
Either paper 3 marks

A school has \(400\) pupils. A sample of \(50\) 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)
Hugo numbers everybody in the population and then uses a random number generator to decide who is in the sample.

(b)
Isla puts everybody in a list and then takes one at equal intervals all the way down it.

(c)
Jonah splits everybody into age groups and then takes a number from each group in proportion to the size of that group.

Show answer

(a) Random sampling (a simple random sample)
(b) Systematic sampling
(c) Stratified sampling

Another like this
Either paper 3 marks

A toy factory makes \(1000\) model cars in a day.

Amara checks the quality of a systematic sample of \(50\) model cars, taken evenly through the day's production.

(a)
Work out how often she should take a model car, so that the \(50\) model cars are spread evenly through the \(1000\).

(b)
Amara says the 50 model cars are a random sample.

Explain why she is wrong.

Show answer

(a) every 20th model car
(b) Once the first model car has been chosen, every other model car in the sample is fixed, so not every group of 50 model cars is equally likely to be chosen.

Another like this
Either paper 3 marks

There are \(800\) students at Tomas's school.

He asks a random sample of \(80\) of them whether they have a school lunch. \(23\) of them say they do.

(a)
Use his sample to estimate how many students at the school have a school lunch.

(b)
Explain why this is only an estimate.

Show answer

(a) \(230\)
(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.

Another like this
Either paper 4 marks

Ms Bhatt is taking a stratified sample of \(40\) students from the \(400\) students in her school.

The table shows how many students are in each year group.

Year group 9 10 11 Total

Number of students 150 170 80 400

(a)
Calculate how many Year \(10\) students should be in the sample.

(b)
Calculate how many Year \(11\) students should be in the sample.

Show answer

(a) \(17\)
(b) \(8\)

Another like this
Either paper 7 marks
Kim works at an airport in the UK. She records the number of planes landing between 11 am and 1 pm each day. The table shows her data for the first 10 days in January.

Day 1 2 3 4 5 6 7 8 9 10

Number of planes 78 88 90 34 77 87 91 88 83 81

(a)
The airport was affected by fog on one of the days.

Which day do you think it was?

Give a reason for your answer.

(b)
Kim uses the data to predict how many planes will land at the airport in a year.

In her method, she uses an estimate of \(83\) planes in each \(2\)-hour period throughout the day. The airport is closed on \(14\) days of the \(365\) days in the year. She assumes the same number of planes land on each day that it is open.

Work out Kim's prediction for the number of planes that will land in a year.

(c)
Give one reason why Kim's prediction may not be reliable.

Show answer

(a) Day 4: only 34 planes landed, much fewer than on any other day (the other nine days were between 77 and 91).
(b) \(349596\ \text{planes}\)
(c) The data are for only 10 days in January, which may not be typical of the whole year; or the 2-hour period from 11 am to 1 pm may not be typical of the rest of the day.

Another like this
Either paper 4 marks

A survey was held at a railway station one day. A sample of the passengers was asked how important a quiet carriage is.

The pie chart shows the answers.

In total there were \(9900\) passengers.

(a)
Estimate how many of the passengers think that a quiet carriage is very important.

Assume that the sample is representative of all the passengers.

(b)
In fact, \(30\%\) of the sample were travelling with young children, but only \(15\%\) of the passengers were travelling with young children.

The people who were travelling with young children are less likely than the others to say that a quiet carriage is very important.

What does this suggest about the actual number of passengers who think a quiet carriage is very important?

Tick one box. Give a reason for your answer by comparing the percentage of the sample with the percentage of the passengers.

☐ higher than your estimate

☐ lower than your estimate

☐ the same as your estimate

Show answer

(a) \(1430\)
(b) Likely to be higher than the estimate: over-represented group, sample 30% against 15%.

Another like this
Either paper 2 marks

Leila wants to find out how people travel to work in she town.

She asks the first 20 people she sees at a bus stop.

(a)
Explain why Leila's sample is likely to be biased.

(b)
Describe one way she could improve the way the sample is chosen.

Show answer

(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.

Another like this

Year group	9	10	11	Total
Number of students	150	170	80	400

Day	1	2	3	4	5	6	7	8	9	10
Number of planes	78	88	90	34	77	87	91	88	83	81

discia.org Sampling and Bias · sheet 1

Answers Sampling and Bias · sheet 1

(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.
The sample leaves out Years 10 and 11. Pupils in those years may differ in how they travel to school, so the sample may not represent all the pupils.
(a) Random sampling (a simple random sample)
(b) Systematic sampling
(c) Stratified sampling
(a) every 20th model car
(b) Once the first model car has been chosen, every other model car in the sample is fixed, so not every group of 50 model cars is equally likely to be chosen.
(a) \(230\)
(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) \(17\)
(b) \(8\)
(a) Day 4: only 34 planes landed, much fewer than on any other day (the other nine days were between 77 and 91).
(b) \(349596\ \text{planes}\)
(c) The data are for only 10 days in January, which may not be typical of the whole year; or the 2-hour period from 11 am to 1 pm may not be typical of the rest of the day.
(a) \(1430\)
(b) Likely to be higher than the estimate: over-represented group, sample 30% against 15%.
(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.

discia.org Sampling and Bias · sheet 1