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Year 10
Higher

Advanced problem solving with sampling

I can use my understanding of sampling to solve problems.

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New
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Year 10
Higher

Advanced problem solving with sampling

I can use my understanding of sampling to solve problems.

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Share activities with pupils
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Lesson details

Key learning points

  1. Samples can be evaluated to determine the validity of any conclusions.
  2. A suitable sample size can vary, depending on the statistical enquiry.
  3. A biased sample can still be useful, such as in stratified sampling.

Keywords

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

  • Stratified sample - A stratified sample is where a representative sample is taken from each stratum.

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

Common misconception

Biased samples are always bad.

A biased sample is sometimes useful if the sample is proportional to the population and/or it focuses on a section of the population relevant to the investigation.

Ask pupils to critique adverts and to check the fine print to discover the data that was collected and analysed to reach the claims of the company. How representative do they think the samples taken are?
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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.
A stratified is where a representative sample is taken from each stratum.
Correct Answer: sample
Q2.
Select all the biased questions.
How many hours gaming did you do last month?
Do you not agree that you are a person who doesn't not play computer games?
How many computer games did you play last month?
Correct answer: Don't you think our new computer game is amazing?
Correct answer: Intelligent people play computer games. Do you play computer games?
Q3.
Jacob writes the question: "How many siblings do you have?". What should Jacob consider when making response boxes for this question?
Have no biased options.
Correct answer: Have a none or 0 option.
Correct answer: Have a "more than" option.
Correct answer: Have no overlaps between options.
Have no leading options.
Q4.
A pizza company asks: In your opinion, how would you rate the sizes of pizza by our rivals?: [Satisfactory, Small, Microscopic]. What is wrong with their question?
Correct answer: The responses are subjective.
The responses are overlapping.
The question has double negatives.
Correct answer: The responses are biased towards negative answers.
Q5.
Select all the questions that are considered to be asking for personal information.
Correct answer: What is your religion?
Correct answer: What is your mark in the last maths test?
How many books did you read last month?
Correct answer: What is your weight?
How many hours of homework did you do last night?
Q6.
A supermarket manager wants to find out how satisfied customers with the store. He asks customers: "Do you not find it easy to not not overspend in this store?". Criticise their question.
The question is leading people to answer 'no'.
The question is biased.
The question is asking for personal information.
Correct answer: The question contains double negatives.

Exit quiz

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6 Questions

Q1.
You should use a sample when the population consists of several distinct groups such as year groups in a school or people studying different courses.
Correct Answer: stratified , stratified
Q2.
A film streaming company designs this questionnaire. How often do you get download films? [once or twice /often / all the time] How could their question be improved?
Correct answer: “Never” option
An option for types of film
Correct answer: A time frame
Correct answer: Unambiguous / clear options
Q3.
The owner of a cinema in Oakfield wants to see if they can expand to the town of Rowanwood. They ask 10 of their friends in Oakfield if they would use a new cinema. How can they improve their sample?
Give questionnaire to people in Oakfield cinema
Correct answer: Take larger sample
Ask more neighbours
Correct answer: Collect data from people in the Rowanwood
Q4.
The owner of a bakers in Oakfield wants to find out what their customers think of their new cakes. Match each type of sample to a suitable example.
Correct Answer:random sample,80 people selected at random from the population of Oakfield

80 people selected at random from the population of Oakfield

Correct Answer:biased sample,80 people selected at random from the baker's customers

80 people selected at random from the baker's customers

Correct Answer:good biased sample ,80 people who buy cakes from the bakers selected at random

80 people who buy cakes from the bakers selected at random

Correct Answer:bad biased sample,80 people who buy gluten free bread at the bakers selected at random

80 people who buy gluten free bread at the bakers selected at random

Q5.
A conservationist collects a stratified sample of 35 birds from a lake. They collect 5 swans, 12 geese, 8 moorhens and some ducks. There are 20 swans on the lake. How many ducks are on the lake?
Correct Answer: 40, 40 ducks, forty, forty ducks
Q6.
A quality controller takes a stratified sample of 16 type A batteries and 12 type B batteries. The factory produce 2545 type A batteries. They produce of type B to the nearest whole battery.
Correct Answer: 1909