[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657306-105":59,"doc-detail-657306-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","summarizing-a-scatter-diagram-five-statistics","Summarizing a Scatter Diagram - Five Statistics","","Summarizing a scatter diagram uses five statistics to describe the pattern of points. The averages and standard deviations of x-values and y-values locate the point cloud and describe its horizontal and vertical spread. The correlation coefficient r quantifies the strength of linear association, reflected in clustering about the SD line. The text also explains how translation and scaling of variables affect standard units and leave r unchanged, while multiplying one variable by a negative number flips the sign.",{"@graph":69,"@context":122},[70,84,105],{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/summarizing-a-scatter-diagram-five-statistics/657306/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/summarizing-a-scatter-diagram-five-statistics/657306.png","ImageObject",300,407,{"name":92,"@type":93},"fresh2021","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What five statistics can summarize a scatter diagram?","Question",{"text":112,"@type":113},"Use the average and SD of the x-values, the average and SD of the y-values, and the correlation coefficient r.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do the averages and SDs help interpret a scatter diagram?",{"text":117,"@type":113},"They specify where the cloud of points is located and how widely it spreads horizontally (x) and vertically (y).",{"name":119,"@type":110,"acceptedAnswer":120},"How do translation and scaling affect the correlation coefficient r?",{"text":121,"@type":113},"Translation and positive scaling do not change standard units, so r remains unchanged; converting between Fahrenheit and centigrade preserves r.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657306,1792977085,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":46},962093912154,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","SUMMARIZING A SCATTER DIAGRAM  \n² A scatter diagram can be summarized by means of ¯ve statistics:  \n² The average and SD of the x-values.  \n² The average and SD of the y-values.  \n² The correlation coe±cient r.  \nThe averages and the SDs specify the location and spread of the cloud of points, horizontally and vertically. The correlation coe±cient measures the amount of linear association, i.e. , clustering about the SD line.  \nAve+2SD  \nAve  \nAve¡2SD  \ny  \n| .\u003Cbr>. .\u003Cbr>.\u003Cbr>.\u003Cbr>. |  | .\u003Cbr>...\u003Cbr>.\u003Cbr>.\u003Cbr>. .\u003Cbr>.. . ..\u003Cbr>.. .\u003Cbr>..\u003Cbr>. .. ..\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>. | .\u003Cbr>.\u003Cbr>. |\n| --- | --- | --- | --- |\n| .\u003Cbr>. .......\u003Cbr>.... .\u003Cbr>. . .\u003Cbr>.\u003Cbr>. ..\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>. . |  | .\u003Cbr>....\u003Cbr>. . |  |\n| .\u003Cbr>|  |  |  |\n\n.  \n.  \n. .  \n.  \n.  \n.  \n.  \n.  \nx  \nAve¡2SD Ave Ave+2SD  \n|~~ ~~ ~~ ~~}  \n{z  \n¼ 95% of the points  \nStrong association Tight clustering Knowing x helps in predicting y Correlation near 1  \nx  \n\n| .\u003Cbr>. .\u003Cbr>.\u003Cbr>.\u003Cbr>. .\u003Cbr>. .\u003Cbr>.\u003Cbr>.. . .\u003Cbr>.\u003Cbr>. .\u003Cbr>. .\u003Cbr>.\u003Cbr>.\u003Cbr>.. |  | .\u003Cbr>. .\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.. . .\u003Cbr>. . . ...\u003Cbr>. | . |\n| --- | --- | --- | --- |\n| .\u003Cbr>... .\u003Cbr>..\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>..\u003Cbr>..\u003Cbr>.\u003Cbr>.\u003Cbr>. . |  | .\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.. .\u003Cbr>.\u003Cbr>. .\u003Cbr>. ..\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>.\u003Cbr>. . |  |\n| .\u003Cbr>. | .\u003Cbr>|  |  |\n\n.  \n.  \n.  \ny  \nAve+2SD  \nAve  \nAve¡2SD  \n9  \n>>  \n=  \n>>  \n;  \nAve¡2SD Ave Ave+2SD  \n|~~ ~~ ~~ ~~}  \n{z  \n¼ 95% of the points  \nWeak association Loose clustering Knowing x isn't much help in predicting y Correlation near 0  \n¼ 95% of the points  \nSOME FEATURES OF THE  \nCORRELATION COEFFICIENT  \n² Look at the following two scatter diagrams. They both show the daily low and high temperatures for Boulder CO for the month of April 1996 . One uses degrees Fahrenheit, the other degrees Centigrade (C = ~~5~~9 (F ¡ 32)) .  \nDaily high (F)  \n80  \n70  \n60  \n50  \n²  \n² ²  \n²  \n²  \n²  \n²²  \n²  \n²²  \n²²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n²  \n20 30 40 50 60  \nDaily high (C)  \n30  \n20  \n10  \n¡ 10 0 10  \nDaily low (C)  \nDaily low (F)  \n² Are the correlation coe±cients the same, or di®erent?² They're the same; r = 0:74 for both diagrams.  \n² To see why, we are going to consider the e®ect of translation (adding the same number to each value of a variable) and scaling (multiplying each value of a variable by the same positive number) on the correlation coe±cient. First we need to consider the e®ect of translation and scaling on standard units.  \n² What e®ect does translation have on standard units?  \nA list  \n2 4 5 6 8 Average  \n.......................................................................................................................................  \n..........................................  \ndeviations from average  \n²  \n.......................................  \n...................................................................................................................................  \n1 SD ............................................................................................................................................................. 1 SD  \nStandard Units  \n¡3=2  \n¡ 1=2  \n0  \n1=2  \n3=2  \nThe same list, translated by 5  \n7 9 10 11 13 Average  \n1 SD ........................................................................................................................................................................ 1 SD  \n² When you shift all the entries on a list by some number,² the average shifts by that number,  \n² the deviations from average don't change,² the standard deviation doesn't change, and ² the standard units don't change.  \n² Standard units are deviations from the average, expressed in units of the SD.  \n² What e®ect does scaling have on standard units?  \nA list  \n2 4 5 6 8 Average  \n.............................................................................................................  \n.....................................  \n² deviations  \nfrom average ..........","cbCaifzvbDr3m2CK","https://ap.wps.com/l/cbCaifzvbDr3m2CK","pdf",93596,"English","# Summarizing a Scatter Diagram\n## Five Key Statistics\n## Correlation and Linear Association\n## Effects of Translation and Scaling\n## Sign Change Under Negative Scaling","[{\"question\":\"What five statistics can summarize a scatter diagram?\",\"answer\":\"Use the average and SD of the x-values, the average and SD of the y-values, and the correlation coefficient r.\"},{\"question\":\"How do the averages and SDs help interpret a scatter diagram?\",\"answer\":\"They specify where the cloud of points is located and how widely it spreads horizontally (x) and vertically (y).\"},{\"question\":\"How do translation and scaling affect the correlation coefficient r?\",\"answer\":\"Translation and positive scaling do not change standard units, so r remains unchanged; converting between Fahrenheit and centigrade preserves r.\"}]","Summarizing a Scatter Diagram - Five Statistics | PDF"]