The Nottingham Emmanuel School Mathematics Department 11 May 2015 To understand different methods of sampling and sample size To identify which sampling

The Nottingham Emmanuel SchoolMathematics Department

18 April 2023

• To understand different methods of sampling and sample size

• To identify which sampling method to use to solve a problem

Key WordsKey Words•population

•sample

•random

•stratified

•bias

SamplingSampling

Lesson ObjectivesLesson Objectives


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Think back to last lesson. Think back to last lesson. What problems did you What problems did you

have sorting through the have sorting through the data?data?


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We can’t possibly use all the data.We can’t possibly use all the data.

We need to cut down the data we We need to cut down the data we use. But we need to do this fairly.use. But we need to do this fairly.

In analysing statistics we usually In analysing statistics we usually use a use a sample sample of the data.of the data.


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CensusCensus

Census research uses data from every Census research uses data from every single member of the population.single member of the population.

If we wanted to do a census study of If we wanted to do a census study of Emmanuel students’ eating habits, we Emmanuel students’ eating habits, we would have to ask EVERY child in the would have to ask EVERY child in the school.school.


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CensusCensus

AdvantagesAdvantages

• Very accurate and reliable data.

DisadvantagesDisadvantages

• Costs a lot of time and money.

• Very difficult to get data for absolutely everybody.


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Random SamplingRandom Sampling

A random sample uses data taken from A random sample uses data taken from some of the population chosen some of the population chosen randomly – every member of the randomly – every member of the population has the same chance of population has the same chance of being chosen.being chosen.

If we wanted to take a random sample of If we wanted to take a random sample of Emmanuel students’, we could put all Emmanuel students’, we could put all the names in a list and then pick every the names in a list and then pick every tenth child to take data from.tenth child to take data from.


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Random SampleRandom Sample

Example:Example:

Kaysey Abbott Daniel Hazledine Ruth Merryweather

Oliver Boot Sarah Hopkins Hayley Rayner

Jack Buckley Holly Hulland Hannah Rodger

Terri-Lee Buckley Christopher Isaac Jessica Ryder

Allistair Burton-Casey Ben Lane Kieran Tetley

Ebony Chambers William Leonard Rhian Thomas

Joshua Coates Colette Leverton Rebecca Voce

Oliver Durner Nicholas Lewin Laura Want

Shannen Fretwell Ross Liggins Iain Watt

Joel George Jack Marriott Andrew Winter

James Greenhalgh Wakas Masood

For this random sample I put all the names in For this random sample I put all the names in alphabetical order and then chose every second child, alphabetical order and then chose every second child, either all the whites or all the yellows.either all the whites or all the yellows.


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Random SampleRandom Sample


• Data is unbiased and reliable.


• Some important parts of the population might be missed out.


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Stratified SampleStratified Sample

A A stratified samplestratified sample divides the population into divides the population into categories and then a random sample can be categories and then a random sample can be taken from each category. The number from taken from each category. The number from each category represents the proportion of each category represents the proportion of the population in that category.the population in that category.

If we wanted to take a If we wanted to take a stratified samplestratified sample of of Emmanuel students’, we could group the Emmanuel students’, we could group the children into male and female and year children into male and female and year groups and then take a sample from each groups and then take a sample from each group.group.


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Example:Example:

MaleMale FemaleFemale

1001 - 1001 - 10041004

Chris Isaac, Will Leonard, Andrew Winter, Joel George, James Greenhalgh, Daniel Hazeldine, Kieran Tetley, Oliver Boot

Total of 8 people we use 4

Terri-Lee Buckley, Sarah Hopkins, Jessica Ryder, Colette Leverton, Kaysey Abbot, Hayley Rayner, Shannen Fretwell, Ruth MerryweatherTotal of 8 people we use 4

1005 - 1005 - 10081008

Jack Buckley, Alistair Burton-Casey, Josh Coates, Oliver Durner, Ben Lane, Nick Lewin, Ross Liggins, Jack Marriott, Wakas Masood, Iain Watt


Ebony Chambers, Holly Hulland, Hannah Rodger, Rhian Thomas, Rebecca Voce, Laura Want


For this stratified sample I’m going to group the For this stratified sample I’m going to group the students based on birth year and sex first. We choose students based on birth year and sex first. We choose at random from each group based on the group’s size.at random from each group based on the group’s size.


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• Ensures that members of all parts of the population are considered.


• More time-consuming and expensive than a random sample.


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Sample sizeSample size

Before we take a sample of the Before we take a sample of the population, we must consider how population, we must consider how large the sample should be.large the sample should be.

Large samples are more likely to be Large samples are more likely to be accurate and representative.accurate and representative.

But, larger samples take longer to sort But, larger samples take longer to sort and may be more expensive to collect.and may be more expensive to collect.


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ActivitiesActivities

1.1. Read through the excellent examples on Read through the excellent examples on page 33 and 34.page 33 and 34.

2.2. Try questions 1, 4 and 5.Try questions 1, 4 and 5.


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For the first part of your Statistics coursework For the first part of your Statistics coursework you will need to test the hypothesis:you will need to test the hypothesis:

““People in Europe live longer than People in Europe live longer than people in Africa.”people in Africa.”

Think about how we could use what we’ve Think about how we could use what we’ve learnt about sampling to help this learnt about sampling to help this investigation – answer the questions on the investigation – answer the questions on the worksheet.worksheet.

HomeworkHomework

Documents

The Nottingham Emmanuel School Mathematics Department 11 May 2015 To understand different methods of sampling and sample size To identify which sampling