[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657399-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-657399-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","frequency-tables","Frequency Tables","","Frequency Tables explains how to summarize data using a frequency distribution and how to extract key statistics such as mean, median, mode, and range from both ungrouped and grouped data. It introduces discrete grouped data using class intervals and midpoints, then applies the same midpoint-based method to continuous grouped data with appropriate class boundaries. The document also covers constructing frequency diagrams, including histograms and frequency polygons, with step-by-step drawing rules.",{"@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/frequency-tables/657399/",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/frequency-tables/657399.png","ImageObject",300,407,{"name":42,"@type":43},"Jasmine","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 is the mean calculated from an ungrouped frequency table?","Question",{"text":62,"@type":63},"Multiply each value x by its frequency f and divide the total by the sum of frequencies. The document uses the standard form mean = Σfx / Σf.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What midpoint method is used for grouped discrete data?",{"text":67,"@type":63},"For each class interval, estimate data values using the class midpoint (halfway between the lower and upper bounds). The mean is then computed using these midpoints weighted by their frequencies.",{"name":69,"@type":60,"acceptedAnswer":70},"How do you draw a frequency polygon from a histogram?",{"text":71,"@type":63},"Join the midpoints of the tops of the histogram bars, then connect extra points on the x-axis at half a class interval before the first bar and after the last bar. Finally, erase the pencil histogram after plotting the polygon.","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},657399,1793072830,{"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":100,"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":143,"read_time":144},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","FREQUENCY TABLES  \n􀁸 Large sets of data are often given in a frequency table  \nExample  \nThis data: 1, 1, 1, 4, 4, 7, 7, 7, 7, 7  \n1 􀀎 1 􀀎 1 􀀎 4 􀀎 4 􀀎 7 􀀎 7 􀀎 7 􀀎 7 􀀎 7 mean 􀀠  \n10  \n􀀠 4.6  \nAnd this frequency table show the same information.  \n\n| x | 1 | 4 | 7 |\n| --- | --- | --- | --- |\n| f | 3 | 2 | 5 |\n\nmean 􀀠 􀀋 3 􀁵 1􀀌 􀀎 􀀋 2 􀁵 4􀀌 􀀎 􀀋 5 􀁵 7􀀌  \n3 􀀎 2 􀀎 5  \n􀀠 4.6  \nThe mean for a frequency table (or frequency distribution can be worked out using the formula  \n􀂦 is the Greek letter S (Sigma) and is used to represent \"the sum of\"  \n􀂦 fx means \"sum of f multiplied by x\"  \n􀂦 f means \"sum of all f\"  \nThe mode can be seen straight way, it is the value Mode=7  \nof x which has the highest frequency, in this case  \nThe range is the difference between the highest and Range = 7 􀀐 1 = 6  \nlowest data values  \nThe median can also be read from a frequency table.  \nExample  \nSome people were asked how many pets they had.  \n\n| Number of Pets (x) | 0 | 1 | 2 | 3 | 4 | 5 |\n| --- | --- | --- | --- | --- | --- | --- |\n| Frequency (f) | 4 | 9 | 3 | 5 | 2 | 0 |\n\nmean 􀀠  \n􀀠  \n􀀠  \n􀂦 fx 􀂦 f  \n4 􀁵 0 􀀎 9 􀁵 1 􀀎 3 􀁵 2 􀀎 5 􀁵 3 􀀎 2 􀁵 4 􀀎 0 􀁵 5  \n4 􀀎 9 􀀎 3 􀀎 5 􀀎 2 􀀎 0  \n38  \n23  \n􀀠 1.65  \nmedian = the middle value.  \n23 people were asked so the middle value is the 12th person. The 12th person has 1 pet.  \n(the 1st four had no pets, the next 9 had 1 pet)  \nMedian = 1 pet  \nMode = 1 pet, the highest frequency.  \nRange = 4 􀀐 0 = 4  \nNote  \nThe above example could have worked out by writing down all of the results as follows:  \n0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4  \nMean: 38 ÷ 23 = 1􀂘65 (2 d.p.)  \nMedian: 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1 , 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4  \nMode: 1  \nRange: 4 􀀐 0 = 4  \nHowever, for very large sets of data, this does become impractical.  \nGROUPED DISCRETE DATA  \n􀁸 When data has been grouped into class intervals, the exact data values are not known.  \n􀁸 The mean can be estimated by using the midpoint of the class interval. The midpoint is the halfway value.  \n􀁸 The modal class is the class interval with the highest frequency.  \nExample  \nThe weights of some students is shown in the following table:  \nModal Class  \nThe modal class is the class interval with the highest frequency,  \nThe modal class = 40 􀁤 W \u003C 45.  \nMean  \nThe table can be extended to show the midpoint as follows:  \nTo work out the midpoint of each class interval, work out  \n½ 􀁵 (upper bound + lower bound) .  \nFor example, the midpoint of the 1st interval = ½ (35 + 30) = ½ 􀁵 65 = 32.5  \nMean (X ) 􀀠 ~~􀂦~~􀂦fxf  \n\n| Weight (kg) | Frequency | Midpoint (x) | fx |\n| --- | --- | --- | --- |\n| 30 􀁤 W \u003C 35 | 4 | 32.5 | 130 |\n| 35 􀁤 W \u003C 40 | 6 | 37.5 | 225 |\n| 40 􀁤 W \u003C 45 | 8 | 42.5 | 340 |\n| 45 􀁤 W \u003C 50 | 2 | 47.5 | 95 |\n| 50 􀁤 W \u003C 55 | 1 | 52.5 | 52.5 |\n|  | 21 |  | 842.5 |\n\nMean = 842.5 ÷ 21 = 40.12 kg (2 d.p.)  \nCONTINUOUS GROUPED DATA  \n􀁸 The mean of a frequency distribution for continuous data is found in the same way as the mean for discrete grouped data. The mid-point of each class interval is used as an estimate for each data value in that interval.  \n􀁸 Care must be taken to find the mid-points of each class interval.  \nExample  \nIf w is the thickness of some books, measured in mm, the class interval 5 􀁤 w \u003C 10 will contain all books from 4.5mm up to 9.5mm.  \n4.5 􀀎 9.5  \nThe mid-point will be 􀀠 7mm .  \n2  \nExample  \nThis frequency distribution shows the thickness of some books.  \n\n| Class Interval (mm) | 5- | 10- | 15- | 20- | 25- | 30- | 35-40 |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| Frequency | 8 | 12 | 14 | 17 | 5 | 3 | 1 |\n\nThe same data could be presented in any of the following ways:  \n\n| Class interval\u003Cbr>(mm) | Frequency |\n| --- | --- |\n| 5 􀁤 w \u003C 10 | 8 |\n| 10 􀁤 w \u003C 15 | 12 |\n| 15 􀁤 w \u003C 20 | 14 |\n| Etc | Etc |\n| 30 􀁤 w \u003C 35 | 3 |\n| 35 􀁤 w \u003C 40 | 1 |\n\nThe mid-point of each class interval is found.  \n\n| Class interval\u003Cbr>(mm) | Frequency |\n| --- | --- |\n| 5 – 10 | 8 |\n| 10 – 15 | 12 |\n| 15 – 20 | 14 |\n| Etc | Etc |\n|","cbCaiuPxBNGSlwnW","https://ap.wps.com/l/cbCaiuPxBNGSlwnW","pdf",266993,"English","# Frequency Tables\n## Mean, Mode, Median, Range from Frequency Tables\n## Grouped Discrete Data\n## Continuous Grouped Data\n## Frequency Diagrams and Frequency Polygons","[{\"question\":\"How is the mean calculated from an ungrouped frequency table?\",\"answer\":\"Multiply each value x by its frequency f and divide the total by the sum of frequencies. The document uses the standard form mean = Σfx / Σf.\"},{\"question\":\"What midpoint method is used for grouped discrete data?\",\"answer\":\"For each class interval, estimate data values using the class midpoint (halfway between the lower and upper bounds). The mean is then computed using these midpoints weighted by their frequencies.\"},{\"question\":\"How do you draw a frequency polygon from a histogram?\",\"answer\":\"Join the midpoints of the tops of the histogram bars, then connect extra points on the x-axis at half a class interval before the first bar and after the last bar. Finally, erase the pencil histogram after plotting the polygon.\"}]","Frequency Tables | PDF",1792978576,15]