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The Nottingham Emmanuel School Mathematics Department 11 May 2015 To understand different methods of sampling and sample size To identify which sampling method to use to solve a problem Key Words population sample random stratified bias Sampling Lesson Objectives

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Think back to last lesson. What problems did you have sorting through the data?

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 We can’t possibly use all the data. We need to cut down the data we use. But we need to do this fairly. In analysing statistics we usually use a sample of the data.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Census Census research uses data from every single member of the population. If we wanted to do a census study of Emmanuel students’ eating habits, we would have to ask EVERY child in the school.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Census Advantages Very accurate and reliable data. Disadvantages Costs a lot of time and money. Very difficult to get data for absolutely everybody.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Random Sampling A random sample uses data taken from some of the population chosen randomly – every member of the population has the same chance of being chosen. If we wanted to take a random sample of Emmanuel students’, we could put all the names in a list and then pick every tenth child to take data from.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Random Sample Example: KayseyAbbottDanielHazledineRuthMerryweather OliverBootSarahHopkinsHayleyRayner JackBuckleyHollyHullandHannahRodger Terri-LeeBuckleyChristopherIsaacJessicaRyder AllistairBurton-CaseyBenLaneKieranTetley EbonyChambersWilliamLeonardRhianThomas JoshuaCoatesColetteLevertonRebeccaVoce OliverDurnerNicholasLewinLauraWant ShannenFretwellRossLigginsIainWatt JoelGeorgeJackMarriottAndrewWinter JamesGreenhalghWakasMasood For this random sample I put all the names in alphabetical order and then chose every second child, either all the whites or all the yellows.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Random Sample Advantages Data is unbiased and reliable. Disadvantages Some important parts of the population might be missed out.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Stratified Sample A stratified sample divides the population into categories and then a random sample can be taken from each category. The number from each category represents the proportion of the population in that category. If we wanted to take a stratified sample of Emmanuel students’, we could group the children into male and female and year groups and then take a sample from each group.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Stratified Sample Example: MaleFemale 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 Merryweather Total of 8 people we use Jack Buckley, Alistair Burton-Casey, Josh Coates, Oliver Durner, Ben Lane, Nick Lewin, Ross Liggins, Jack Marriott, Wakas Masood, Iain Watt Total of 10 people we use 5 Ebony Chambers, Holly Hulland, Hannah Rodger, Rhian Thomas, Rebecca Voce, Laura Want Total of 6 people we use 3 For this stratified sample I’m going to group the students based on birth year and sex first. We choose at random from each group based on the group’s size.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Stratified Sample Advantages Ensures that members of all parts of the population are considered. Disadvantages More time- consuming and expensive than a random sample.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Sample size Before we take a sample of the population, we must consider how large the sample should be. Large samples are more likely to be accurate and representative. But, larger samples take longer to sort and may be more expensive to collect.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 Activities 1.Read through the excellent examples on page 33 and Try questions 1, 4 and 5.

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The Nottingham Emmanuel School Mathematics Department 11 May 2015 For the first part of your Statistics coursework you will need to test the hypothesis: “People in Europe live longer than people in Africa.” Think about how we could use what we’ve learnt about sampling to help this investigation – answer the questions on the worksheet. Homework

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