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Further worksheets guide students through tasks on sampling, stratified and quota samples, estimating population mean/variance from samples, and interpreting hypothesis-driven changes in mean CO2 emissions across 2002 and 2016.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/getting-real-with-statistics-a-level-maths-mathsconf-31-resource-booklet/619140/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/getting-real-with-statistics-a-level-maths-mathsconf-31-resource-booklet/619140.png","ImageObject",300,407,{"name":42,"@type":43},"Lucas Martin","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-10-20",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you check whether the 2002 or 2016 NOX samples contain outliers from boxplots?","Question",{"text":63,"@type":64},"Use the definition of an outlier as a value more than 1.5 times the IQR below Q1 or above Q3. Compare the boxplot whiskers and points against that rule to decide if either sample has outliers.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What assumptions must be made to support claims about reductions in NOX emissions or differences between petrol and diesel?",{"text":68,"@type":64},"Rose must assume the evidence from the graphs is representative and comparable across time. Julian must assume the distributions shown allow an environmental comparison between petrol and diesel, supporting the claim that petrol engines are much better.",{"name":70,"@type":61,"acceptedAnswer":71},"How do students estimate population quantities from sample data in the sampling activities?",{"text":72,"@type":64},"They take specified samples (e.g., diesel cars or petrol Toyotas), calculate summary statistics such as mean and standard deviation where required, then use those values to estimate the mean, variance, or other population measures for the relevant group in the LDS.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},619140,1792525420,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":112,"preview_page_count":4},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Getting real with statistics  \nA-level MATHS  \nMathsConf 31  \nResource booklet  \nPublished: Spring 2023  \nThe content of this training course contains no reference to future exam content as far as we know at the time of production.  \n| Contents | Page |\n| --- | --- |\n| Introductory Activity | 4 |\n| Activity 1 | 6 |\n| Activity 2 | 7 |\n| Activity 3 | 8 |\n| LDS as a sample | 9 |\n\nIntroductory activity  \nNOX emissions for diesel cars registered in NW in 2002 (above) and in 2016 (below)  \n• An outlier is defined as a value more than 1.5 times the IQR below Q1 or above Q3  \n• Determine whether either of the samples represented in these boxplots contains any outliers.  \n• Using information from the boxplots find an appropriate value for the percentage reduction in NOX emissions between 2002 and 2016.  \n• Rose claims that these graphs show there was a very large reduction in the NOX emissions of cars in the UK.  \n• What assumptions would Rose have to make to support her claim, based on these graphs?  \nNOX emissions for cars registered in NW in 2016 – diesel (above) and petrol (below)  \n• Compare the distributions of NOX emissions for diesel and petrol cars.  \n• Julian claims that, based on this evidence, petrol engines are much better for the environment than diesel engines. He says that the proposed ban on diesel engines is justified.  \n• What assumptions must Julian make, based on this evidence, to support his claim?  \nActivity 1  \nThe following worksheets and activities are extracts from AQA’s LDS Teaching  \nGuidance.  \nWorksheet LDS1: Exploring the LDS  \n1 How many cars are included in the LDS?  \n2 What makes of car are included and why?  \n3 How many electric powered cars are there?  \n4 How many cars have owners in the North West region?  \n5 How many cars have female registered keepers?  \n6 How many are company cars?  \n7 What is the largest engine size?  \n8 How many cars were registered in 2012?  \n9 What makes are the cars with the lowest carbon dioxide emissions?  \n10 What is the highest level of carbon monoxide emissions?  \n11 How many vehicles have nitrogen oxide emissions less than 0.01 g/km?  \n12 What is the highest level of particulate emissions?  \n13 What is the actual mass of the car with the largest mass?  \n14 What make is the car with the highest hydrocarbon emissions?  \n15 Jamie drives a BMW to work and home each day. Each journey is approximately 40 miles. Estimate the total CO2 emissions from Jamie’s car per annum by finding the average CO2 emissions for all BMWs in the LDS.  \nActivity 2  \nWorksheet LDS 2: Sampling from the Cars LDS  \n1 Take a sample of 50 diesel powered cars.  \na. For how many of these cars is there data on their particulate emissions.  \nb. Use this data to make an estimate of the median particulate emissions of diesel cars in the LDS.  \n2 Take a sample of 100 petrol powered Fords.  \na. Find the mean and standard deviation of the carbon monoxide emissions of these cars.  \nb. Use your values to make estimates of the mean and variance of the carbon monoxide emissions of all petrol-powered Fords in the LDS.  \n3 In the LDS 26% of cars are registered in London, 30% in the North West and 44% in the South West. Petra wants to take a stratified random sample of 375 cars from the LDS with her strata being the three regions.  \nHow many cars should she select from each region?  \n4 The table shows the number of cars in the LDS broken down by make and year of registration.  \n\n| Make | 2002 | 2016 |\n| --- | --- | --- |\n| BMW | 141 | 410 |\n| Ford | 407 | 682 |\n| Toyota | 154 | 121 |\n| Vauxhall | 260 | 809 |\n| Volkswagen | 337 | 506 |\n\nCharley is taking a quota sample of cars from the LDS. She will take a sample of 50 for each year of registration, with 10 of each make.  \na. Explain whether Charley’s sample is representative of the population.  \nGuillermo takes a sample of 50 petrol-powered Toyotas from the LDS. Otis takes a sample of 100 petrol-powered Toyotas.  \nGuillermo calculates the mean CO2 emissions to be 16","cbCaite8v3glL5R3","https://ap.wps.com/l/cbCaite8v3glL5R3","pdf",514793,12,"English","# Introductory Activity\n## NOX emissions: outliers, percentage reduction, and assumptions\n## NOX distributions: diesel vs petrol and environmental claims\n# Activity 1\n## Worksheets: LDS1 exploring the LDS\n# Activity 2\n## Worksheets: LDS 2 sampling from the Cars LDS\n# Activity 3\n## Investigating hypotheses and interpreting results\n# The LDS as a sample","[{\"question\":\"How do you check whether the 2002 or 2016 NOX samples contain outliers from boxplots?\",\"answer\":\"Use the definition of an outlier as a value more than 1.5 times the IQR below Q1 or above Q3. Compare the boxplot whiskers and points against that rule to decide if either sample has outliers.\"},{\"question\":\"What assumptions must be made to support claims about reductions in NOX emissions or differences between petrol and diesel?\",\"answer\":\"Rose must assume the evidence from the graphs is representative and comparable across time. Julian must assume the distributions shown allow an environmental comparison between petrol and diesel, supporting the claim that petrol engines are much better.\"},{\"question\":\"How do students estimate population quantities from sample data in the sampling activities?\",\"answer\":\"They take specified samples (e.g., diesel cars or petrol Toyotas), calculate summary statistics such as mean and standard deviation where required, then use those values to estimate the mean, variance, or other population measures for the relevant group in the LDS.\"}]","Getting real with statistics - A-level MATHS - MathsConf 31 - Resource booklet | PDF",1792462529]