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The candidate must complete all questions in the provided spaces using black ink, showing working clearly. The paper contains six questions with marks totalling 50, covering statistical measures and probability, including Spearman’s rank correlation, interpretation of correlation results, means for ranked data, and drawing and determining a line of best fit for a bivariate plot. A formula sheet and normal probability table are provided.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/gcse-further-mathematics-unit-3-statistics-with-calculator-paper/207493/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Logic","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What are the key instructions for answering this GCSE Further Mathematics statistics paper?","Question",{"text":106,"@type":107},"Write the centre and candidate numbers in the provided spaces, answer in the spaces given, use black ink only, and show all working clearly. All six questions must be answered.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"Which statistical methods are included in the provided formula sheet?",{"text":111,"@type":107},"The formula sheet includes statistical measures such as mean and standard deviation, probability rules, and Spearman’s coefficient of rank correlation. It also provides quadratic solution formulas and additional related expressions.",{"name":113,"@type":104,"acceptedAnswer":114},"What does Question 1 require students to do with the singing contest data?",{"text":115,"@type":107},"Students must write rank orders for two songs, calculate Spearman’s rank correlation, interpret the result, find the mean marks for each song, draw a line of best fit on a scatter graph, and determine its equation.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},207493,1788599771,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","General Certificate of Secondary Education 2023  \nCentre Number  \n\n|  |  |  |  |  |\n| --- | --- | --- | --- | --- |\n\nCandidate Number  \n\n|  |  |  |  |\n| --- | --- | --- | --- |\n\nFurther Mathematics  \nUnit 3 (With calculator) Statistics  \n[GFM31]  \nFRIDAY 23 JUNE, AFTERNOON  \nMV18  \nTime  \n1 hour, plus your additional time allowance.  \nInstructions to Candidates  \nWrite your Centre Number and Candidate Number in the spaces provided at the top of this page.  \nYou must answer the questions in the spaces provided.  \nComplete in black ink only.  \nAll working must be clearly shown in the spaces provided. Marks may be awarded for partially correct solutions.  \nWhere rounding is necessary give answers correct to 2 decimal places unless stated otherwise. Answer all six questions.  \nInformation for Candidates  \nThe total mark for this paper is 50.  \nFigures in brackets printed at the end of each question indicate the marks awarded to each question or part question.  \nYou may use a calculator.  \nThe Formula Sheet is on page 2 and the Normal Probability Table is on the Insert provided.  \nFormula Sheet  \nStatistics  \nStatistical measures: Mean = RRffx  \nStandard deviation =  ~~ ~~R~~ ~~fRxf2 –(x~~ ~~ ) 2  \nwhere x is the mean  \nProbability: P(A \u003C B) = P(A) + P(B)– P(A > B)  \nP(A * B) = P(AP~~(~~~~) ~~B)  \nBivariate Analysis: Spearman’s coefficient of rank correlation  \nis given by  \nr = 1 – n~~ 6~~(nR2–d~~ ~~21)  \nQuadratic equations: If ax2 + bx + c = 0 (a ≠ 0)  \nthen x = –b~~ ~~±~~ ~~b22a~~ ~~–~~ ~~4ac~~ ~~  \nBlank Page  \n(Questions start overleaf)  \n13360.03 MV18  \n3  \n[Turn over  \n1 At a singing contest eight competitors were scored on each of two songs.  \nThe table below shows their scores for each song.  \n\n| Harry | 75 | 72 |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| Gail | 66 | 71 |  |  |  |  |\n| Fred | 76 | 69 |  |  |  |  |\n| Eve | 73 | 70 |  |  |  |  |\n| David | 65 | 69 |  |  |  |  |\n| Carol | 64 | 66 |  |  |  |  |\n| Brian | 78 | 75 |  |  |  |  |\n| Ann | 71 | 68 |  |  |  |  |\n| Competitor | First song | Second song | Ranks\u003Cbr>( F irst song) | Ranks\u003Cbr>(Second song) |  |  |\n\n(i) Write down, in the table opposite, the rank orders for the first and second songs. [2 marks]  \n(ii) Calculate Spearman’s coefficient of rank correlation.[4 marks]  \nAnswer    \n(iii)Interpret your answer to part (ii) . [1 mark]  \nAnswer    \n13360.03 MV18  \n5  \n[Turn over  \n(iv)Calculate the mean mark for the first song and the mean mark for the second song. [1 mark]  \nAnswer Mean first song    \nMean second song    \nThe data from the table are plotted on the graph below.  \nSecond song  \n80  \n75  \n70  \n×  \n×  \n×  \n×  \n×  \n×  \n×  \n×  \n65  \n60  \n60 65 70 75 80  \nFirst song  \n(v) Draw your line of best fit on the graph. [2 marks]  \n13360.03 MV18  \n7  \n[Turn over  \n(vi)Determine the equation of the line of best fit which you have drawn. [3 marks]  \nAnswer    \nBlank Page  \n(Questions continue overleaf)  \n13360.03 MV18  \n9  \n[Turn over  \n2 The speeds of 10 cars and 4 lorries were recorded in a  \n30 mph zone on a road.  \nFor all 14 vehicles, the mean speed was 32 mph and the standard deviation was 4 mph.  \nThe speeds of the lorries were 28 mph, 30 mph, 33 mph and 40 mph.  \nCalculate  \n(i) the mean speed of the cars, [2 marks]  \nAnswer   mph  \n13360.03 MV18 10","cbCaich0f3cJWCUs","https://ap.wps.com/l/cbCaich0f3cJWCUs","pdf",384288,28,"English","# Instructions to Candidates\n## Formula Sheet (Statistics)\n## Questions\n### Question 1\n### Question 2","[{\"question\":\"What are the key instructions for answering this GCSE Further Mathematics statistics paper?\",\"answer\":\"Write the centre and candidate numbers in the provided spaces, answer in the spaces given, use black ink only, and show all working clearly. All six questions must be answered.\"},{\"question\":\"Which statistical methods are included in the provided formula sheet?\",\"answer\":\"The formula sheet includes statistical measures such as mean and standard deviation, probability rules, and Spearman’s coefficient of rank correlation. It also provides quadratic solution formulas and additional related expressions.\"},{\"question\":\"What does Question 1 require students to do with the singing contest data?\",\"answer\":\"Students must write rank orders for two songs, calculate Spearman’s rank correlation, interpret the result, find the mean marks for each song, draw a line of best fit on a scatter graph, and determine its equation.\"}]","GCSE Further Mathematics Unit 3 - Statistics (With calculator) - Paper | PDF",71]