[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657404-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-657404-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","statistical-diagrams-starter","Statistical diagrams - Starter","","Starter lesson material on statistical diagrams for GCSE-level maths, covering cumulative frequency to estimate the median and interquartile range, and calculate percentages within mark intervals. Includes guidance and examples for stem-and-leaf (ordered and back-to-back) diagrams, histograms using frequency density, cumulative frequency graphs with steps for drawing the curve, and box-and-whisker plots. Ends with advice for interpreting spread and central tendency when comparing groups.",{"@graph":14,"@context":72},[15,34,55],{"@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/statistical-diagrams-starter/657404/",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/statistical-diagrams-starter/657404.png","ImageObject",300,407,{"name":42,"@type":43},"Aldword","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"How do you estimate the median and interquartile range using cumulative frequency?","Question",{"text":62,"@type":63},"Draw or interpret a cumulative frequency curve and use the appropriate cumulative frequency positions to read off the median and quartiles. Then compute IQR as Q3 minus Q1.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What is an ordered stem-and-leaf diagram and what key must be included?",{"text":67,"@type":63},"Values are written in ascending order within each stem row, and a key is required to show how to interpret stems and leaves. For example, the tens digits form stems and the units digits form leaves.",{"name":69,"@type":60,"acceptedAnswer":70},"How is a histogram constructed and how do you use it to find frequencies?",{"text":71,"@type":63},"The bar area represents frequency. Use frequency density on the vertical scale, then calculate the number of cars (or proportion) in each class interval using the relevant bar areas.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},657404,1792978584,{"code":4,"msg":81,"data":82},"success",[83,87,91,94,99,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":92,"slug":93},70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"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":95,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"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":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":123},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Statistical diagrams  \nStarter  \n1. (Review of GCSE material)  \nConsider the cumulative frequency for the number of marks gained by a year group ina maths exam.  \n(a) Estimate the median.  \n(b) Estimate the interquartile range.  \n(c) Calculate the percentage of students who scored between 45 and 75 marks  \nNotes  \nStem and leaf diagrams  \nA stem and leaf diagram is a great way to express a small amount of raw data clearly when each data value must be included.  \nThe data values for the time to travel to school of a group of students is below…  \n12, 26, 9, 17, 14, 28, 11, 31, 23, 19, 15, 20  \n…written in a stem and leaf diagram would look like this:  \nTime taken to travel to school (min)  \nThe tens digits form the stems.  \n0 9  \n1 1 2 4 2 0 3 6  \n3 1  \nKey: 2 | 6 means 26  \n5  \n8  \n7 9  \nThe units digits form the leaves.  \nEach stem and leaf diagram must include a key that explainshow to interpret values.  \nSince the values are put in ascending order in each row, it is called an ordered stem and leaf diagram. When asked to create a stem and leaf diagram, assume it must be an ordered stem and leaf diagram.  \nA number in brackets is sometimes written at the end of the each row —this indicates how many data values there are in each row, which is useful when there are lots of values.  \nLength of time (sec)  \n1  \n2  \n3  \n8  \n2  \n3  \n9  \n4  \n7  \n(3)  \n9 (5)  \n(2)  \nKey: 1 | 5 means 1.5  \n[www.mathspanda.com](www.mathspanda.com)  \nE.g. 1 (a) The weights of a group of students were recorded as:  \n55, 67, 43, 46, 51, 81, 64, 52, 74, 57, 63, 68, 57, 77 Express this data points in a stem and leaf diagram.  \n(b) State the value of the mode for the data.  \n(c) Use your diagram to state the median for the data.  \nBack-to-back stem and leaf diagrams  \nTwo sets of data values can be compared using a back-to-back stem and leaf diagram.  \nBelow shows the heights of a sample of students from Year 8 and Year 9.  \n\n| Year 8 |  | Year 9 |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| 7 6 3 0 | 15 | 9 | 9 |  |  |\n| 8 5 4 4 2 | 16 | 1 | 3 | 8 |  |\n| 7 5 2 | 17 | 0 | 3 | 4 | 7 9 |\n| 0 | 18\u003Cbr>19 | 2\u003Cbr>2 | 5 | 6 | 8 |\n\nKey: 15 | 9 means 159  \nN.B. The values on the left-hand side of the diagram are in descending order i.e. the digits closest to the centre are the smallest.  \nE.g. 2 Answer these questions on the back-to-back stem and leaf diagram above.  \n(a) State the height of the largest student in Year 9.  \n(b) State the height of the smallest student in Year 8  \n(c) Comment on how the table would look different if samples of Year 12 and Year 13 students were taken. Think of two ways it could be different. Give a reason for your answer.  \nHistograms  \nArea of bar = frequency of the group  \nThe formula for the vertical scale, frequency density is: Frequency density = ~~ ~~FClrequeass~~ ~~wnicdtyh  \nE.g. 3 Consider the histogram to the right showing the speeds of cars on the M1 .  \n(a) Calculate the number of cars that were travelling between 50 and 60 mph.  \n(b) Calculate the percentage of cars that were breaking the speed limit of 70 mph.  \n(c) Calculate the percentage of cars that were travelling less than 50 mph.  \n(d) Calculate an estimate for the mean of the data.  \n[www.mathspanda.com](www.mathspanda.com)  \nCumulative frequency graphs  \nWhen data is presented as table of grouped values (e.g. 10 ≤ h \u003C 20) a cumulative frequency graph can be drawn to estimate the median and quartiles. In the AS or A2 examination, it is unlikely you’ll be asked to draw a cumulative frequency curve due to time constraints. The method is provided here for completeness.  \nSuccess Criteria —drawing a cumulative frequency curve:  \n1. Add an extra column to the table and find the cumulative frequency.  \n2. Draw the axes — cumulative frequency is always on the vertical axis. Label your axes, make sure there is a suitable title on the axes.  \n3. The line must start from the horizontal axis. The left-hand value of the first interval is the first number on the horizontal ax","cbCaie7bhNkPjskm","https://ap.wps.com/l/cbCaie7bhNkPjskm","pdf",348684,"English","# Starter\n## Cumulative frequency for marks gained\n## Stem and leaf diagrams\n## Back-to-back stem and leaf diagrams\n## Histograms\n## Cumulative frequency graphs\n## Box and whisker plots\n## Comparing groups using median and IQR","[{\"question\":\"How do you estimate the median and interquartile range using cumulative frequency?\",\"answer\":\"Draw or interpret a cumulative frequency curve and use the appropriate cumulative frequency positions to read off the median and quartiles. Then compute IQR as Q3 minus Q1.\"},{\"question\":\"What is an ordered stem-and-leaf diagram and what key must be included?\",\"answer\":\"Values are written in ascending order within each stem row, and a key is required to show how to interpret stems and leaves. For example, the tens digits form stems and the units digits form leaves.\"},{\"question\":\"How is a histogram constructed and how do you use it to find frequencies?\",\"answer\":\"The bar area represents frequency. Use frequency density on the vertical scale, then calculate the number of cars (or proportion) in each class interval using the relevant bar areas.\"}]","Statistical diagrams - Starter | PDF"]