Quota, cluster and other samples
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Do Now
The first question is what today's lesson needs. The others bring back earlier topics.
- A1Needed today[2 marks]
A systematic sample of 50 is taken from a list of patients of 1500 names, numbered 1 to 1500. The random start is 24. Write down the number of the last name chosen.
Answer - A2Last lesson[2 marks]
A cinema's members has 4500 people, and 475 of them are students. A stratified sample of 150 is taken. How many students are in the sample?
Answer - A3Maths skill[2 marks]
Write as a mixed number in its simplest form.
Answer - A4Maths skill[2 marks]
A car is worth £. Its value falls by each year. Find its value after 2 years.
Answer
Examples, then your turn
Your teacher works through each example with you. Then try the one beside it.
Name the sampling method in each case.
(a) A researcher chooses 6 of the 40 primary schools in a county at random and asks every teacher in those 6 schools.
(b) A reporter asks the first 30 people she meets outside a station.
(c) A TV show asks viewers to text in their vote.
- B1[3 marks]
Name the sampling method in each case.
(a) An interviewer must find 25 men and 25 women aged over 60, and she chooses who to ask.
(b) A teacher picks the 10 students she thinks are most typical of her class.
(c) A clerk takes every 15th name on a list, after a random start.
Answer
In a town, 46% of adults are under 40. A researcher takes a quota sample of 150 adults by age. How many adults under 40 does she ask, and how does she choose them?
- B2
A cinema has 1800 customers a week: 810 adults, 540 students and 450 children. The manager takes a quota sample of 60 customers.
(a)[2 marks]Work out the quota for each group.
Answer(b)[1 mark]Give one advantage of a quota sample here.
(c)[1 mark]Explain why it is not a random sample.
Total for B2: 4 marks
A supermarket chain has 80 stores. To survey its staff, it chooses 4 stores at random and asks every member of staff in those 4 stores. Give one advantage and one disadvantage of this cluster sample.
- B3[2 marks]
A council wants to know what households think of bin collections in its 30 villages. It chooses 3 villages at random and asks every household in them. Give one advantage and one disadvantage of this method.
A student wants to know how much exercise the adults in her town do. She asks people in a gym. Explain why this sample is biased.
- B4[2 marks]
A newspaper wants to know how adults in a city travel to work. It asks people at the main train station at 8 am. Explain why this sample is biased.
Kim wants the views of the residents of her town on a new skate park. She stands outside the youth club on a Friday evening and asks 25 people under 18 and 25 people aged 18 or over. Assess her plan.
- B5[3 marks]
Tom wants to find the mean amount families in his town spend on food each week. He posts a link on the town's online forum and uses the first 100 replies. Assess Tom's plan.
Practice
- C1[2 marks]
A radio station asks listeners to phone in if they think the speed limit on a road should be lowered. Of the callers, 82% say yes. Explain why this may not show what all the listeners think.
- C2[2 marks]
A head teacher chooses 12 students she thinks represent the school for a group about the school day. Give one advantage and one disadvantage of this judgement sample.
- C3[2 marks]
A college emails a survey about its canteen to 600 students. Only 90 reply. Explain why the results may be biased.
- C4[2 marks]
Sam says, "A quota sample is just as good as a stratified sample, because both have the right number from each group."
Explain why Sam is wrong.
Exam-style questions
- D1[2 marks]
Ben says, "My quota sample does not need a sampling frame, so it cannot be biased."
Explain why Ben is wrong.
- D2
A delivery company wants the views of 300 of its customers. It has 9 depots. It thinks about three methods.
Method A: choose 2 of the 9 depots at random and ask every customer of those depots.
Method B: number all the customers and use random numbers to choose 300.
Method C: put a link to a survey on the company's website.
(a)[2 marks]Name each method.
Answer(b)[3 marks]Which method should the company use? Give reasons, commenting on the other two methods.
Total for D2: 5 marks - D3[4 marks]
Ana wants to find out how many hours of television adults in her town watch each week. She uses a quota sample of 40 men and 40 women, and she asks people in the town's shopping centre on a Tuesday afternoon. Assess Ana's plan, and suggest one improvement. You must give a conclusion.
Extension
No route is given. The hints are at the end of the sheet. Use one at a time.
- E1[3 marks]
A quota sample of 200 adults is taken by gender and age. In the town, 45% of adults are men. 40% of the men and 30% of the women are under 30. How many adults aged 30 or over should be in the sample?
Hint 1 · What to try
Find how many men and how many women are in the sample first.
Hint 2 · The first line
There are men and women, so men and women are under 30.
Hint 3 · The full method
are under 30, so subtract from 200.
Answer
How did it go?
Colour one circle on each line.| Not yet | Nearly | Yes | |
|---|---|---|---|
| I can name quota, cluster, convenience, judgement and self-selecting samples. | |||
| I can work out quotas and explain why a quota sample is not random. | |||
| I can assess a sampling plan by its location and its method, and improve it. |
Answers and mark scheme
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