Mia asks a sample of 40 students how they travel to school. 12 of the students in the sample walk to school.
Work out an estimate for the number of students at the school who walk to school.
2 marks
Show answer
240
2
1200 people visited a supermarket one Saturday.
A manager took a sample of 50 of these people. 18 of the people in the sample used a discount voucher.
Work out an estimate for the total number of people who used a discount voucher that Saturday.
Write down one assumption you made in working out your estimate.
3 marks
Show answer
a) 432b) The sample is representative of all the people who visited
3
Mo wants to find out which sport the students in his school like best. There are 600 students. He asks 5 of his friends in the school football team.
Give two reasons why this is not a good way to choose a sample.
2 marks
Show answer
The sample is too small (only 5 of 600). The sample is biased: his friends in the football team are likely to prefer football, so they do not represent all the students.
4
A town has 5600 residents.
A council officer asks a sample of 80 residents whether they support a new cycle lane. 28 of the residents in the sample support the cycle lane.
Work out an estimate for the number of residents of the town who support the cycle lane.
State one assumption you made. Explain how your estimate would be affected if the assumption is not true.
3 marks
Show answer
a) 1960b) The sample is representative; if not, the estimate would be unreliable
5
A farm packs apples in batches of 1500.
A quality checker takes a sample of apples from a batch. She finds that 3 out of every 20 apples in the sample are bruised.
Work out an estimate for the number of bruised apples in the batch.
Give one reason why the estimate might not be reliable.
3 marks
Show answer
a) 225b) The sample may not be representative of the batch (or it may be too small)
6
A sports club has 480 members: 192 juniors and 288 seniors.
Grace takes a stratified sample of 50 members, by junior or senior.
Work out how many juniors and how many seniors should be in the sample.
3 marks
Show answer
juniors) 20seniors) 30
7
A television show asks viewers to vote by phone on whether the town should build a new swimming pool. 3000 people phone in and 2400 of them vote yes. The presenter says, "80% of people in the town want a new pool."
Give two reasons why the presenter's statement may not be correct.
3 marks
Show answer
Only people who watch the show and chose to phone could vote, so the sample is not random or representative of the whole town. People with strong opinions are more likely to phone, and people can phone more than once or live outside the town.
8
Ben wants to find out how many of the 3400 adults in a village travel to work by car.
Ben plans to survey adults standing on the platform at the village railway station at 8 am. Explain why this sample is likely to be biased.
Instead, Ben surveys a fair sample of 120 adults from the village. 42 of them travel to work by car. Work out an estimate for the number of adults in the village who travel to work by car.
3 marks
Show answer
a) People at a railway station at 8 am are mostly commuting by train, so car users would be under-representedb) 1190
9
A leisure centre has 2400 members.
The manager takes a random sample of 60 members.
24 of the members in the sample are female.
15 of the members in the sample are female members who attend a fitness class each week.
Work out an estimate for the number of female members of the leisure centre.
Work out an estimate for the number of members who are female and attend a fitness class each week.
3 marks
Show answer
a) 960b) 600
10
There are 450 students in Year 9: 240 boys and 210 girls.
Priya wants a stratified sample of 60 students, by gender.
Work out how many boys and how many girls should be in the sample.
Priya asks the 32 boys and 28 girls in her sample whether they would join a coding club. 15 of the boys and 14 of the girls say yes. Work out an estimate for the number of Year 9 students who would join the club. Give your answer to the nearest whole number.
3 marks
Show answer
a) 32 boys and 28 girlsb) 218
11
A school has 900 students. The head teacher wants a random sample of 30 students.
The names of all the students are on an alphabetical list.
Describe a method she could use to select a random sample of 30 students.
3 marks
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Number the students 1 to 900 down the list. Use a random number generator to produce numbers between 1 and 900, ignoring repeats, until 30 different numbers are chosen. The students with those numbers form the sample.
12
A factory fills 5000 jars of jam each day.
One day, a supervisor checks a sample of 150 jars. 6 of the jars in the sample are underfilled.
Work out an estimate for the number of underfilled jars filled that day.
The sample of 150 jars was taken during the first hour of production only. Explain why this could make the estimate unreliable.
3 marks
Show answer
a) 200b) The sample only covers the first hour, so it may not be representative of the whole day's production
13
Jo wants to estimate how many of the 1800 students at her school would buy food from a new salad bar.
She asks a sample of 90 students. 54 of them say they would buy food from the salad bar.
Work out an estimate for the number of students at the school who would buy food from the salad bar.
Jo only asked students in Year 7. Explain how this could affect your estimate.
Describe one way Jo could improve her sample.
4 marks
Show answer
a) 1080b) Year 7 students may have different tastes from other year groups, so the sample is biased and the estimate may be too high or too lowc) Choose students at random from every year group (a random sample of the whole school)
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.