[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-497894-105":59,"doc-detail-497894-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","numerical-reasoning-formula-sheet-averages-percentages-ratios","Numerical Reasoning Formula Sheet - Averages, Percentages, Ratios","","Numerical Reasoning Formula Sheet provides clear, step-by-step formulas for key exam-style topic areas: averages, weighted averages, percentages (including percentage change and increase/decrease), reverse percentage calculations, and ratios. It explains core definitions, highlights common traps such as weighting when combining averages, and supplies worked practice questions using representative datasets, values, and totals. Includes ratio splitting using Y:Z with total items to determine each part.",{"@graph":69,"@context":123},[70,84,106],{"@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/numerical-reasoning-formula-sheet-averages-percentages-ratios/497894/",{"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/numerical-reasoning-formula-sheet-averages-percentages-ratios/497894.png","ImageObject",300,407,{"name":92,"@type":93},"Fans","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-02",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you calculate a standard average (mean) from a set of values?","Question",{"text":113,"@type":114},"Add all values in the dataset and divide by the number of values. The mean represents the dataset total per item.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why can’t you average two percentages by taking the simple middle value?",{"text":118,"@type":114},"When combining results, weighting matters because each average may represent a different number of values. You must weight by how many items each average covers (e.g., 15 vs 5 children).",{"name":120,"@type":111,"acceptedAnswer":121},"How do you use a ratio like Y:Z to find the number of each part from a total?",{"text":122,"@type":114},"Compute Number of Y = (Y ÷ (Y + Z)) × Total items. With a 7:3 ratio and total 80, this yields 56 for the Y part.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},497894,1791362201,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},5909892330395,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","NUMERICAL  \nREASONING  \nFORMULA  \nSHEET  \nCONTENTS:  \n◊ AVERAGES  \n◊ PERCENTAGES  \n◊ RATIOS  \nAverages  \nThe average, or ‘mean’, is found by adding up all the values in the dataset and dividing the total by the number of values.  \nAverage = ~~ ~~􀯇~~ ~~􀯌􀯨􀯨􀯠􀯠􀯕􀯘􀯢􀯥􀯙􀯢􀯏􀯙􀯔􀯟􀯏􀯨􀯔􀯘􀯦􀯟􀯨􀯘􀯦  \nLet’s go through a quick practice question…  \nQ: What is the average of the following data set?  \nData set: 4, 27, 60, 90, 133  \nAverage = ~~ ~~4,~~ ~~27,~~ ~~605,~~ ~~90,~~ ~~133  \nAverage = 62.8  \nThere are also weighted averages, do not be fooled into thinking the question is asking for a standard average – these are different.  \nWeighted Average = 􀯌􀯨~~ ~~􀯠􀯇􀯢􀯨􀯙􀯠􀯐􀯘􀯜􀯕􀯘􀯥􀯚􀯢ℎ􀯙􀯧􀯘􀯏􀯗􀯔􀯟􀯏􀯨􀯔􀯘􀯟􀯦􀯨􀯘􀯦  \nWe will go through an example question which will highlight the importance of being able to identify a weighted value question.  \nQ: 15 school children take a test and score an average of 70% between them. The next day 5 more children take the same test and score an average of 80% . What is the combined average score for all these children?  \nNow it may seem tempting to say the average is 75% because the two averages are 70 and 80, and 75 is in the middle right?  \nHowever, this doesn’t consider the weight of the two averages…  \nThere are 15 children who make up the 70% average, compared with 5 children generating the 80% average.  \nAs the 70% average score contains a larger number of values, we must weight our new average accordingly .  \nSum of weighted values = ( 15 x 70 ) + ( 5 x 80 )  \n= 1450  \nWeighted Average = ~~ ~~145200  \n= 72.5%  \nPercentages  \nPercent literally means ‘per 100’. When we work out percentages, we are presenting a number as parts per hundred.  \nPercent = ~~ ~~􀯏􀯍􀯔􀯢􀯟􀯧􀯨􀯔􀯘􀯟~~ ~~ x 100  \n| The difficulty with percentages arises when we must work out percentage changes and increases/decreases .\u003Cbr>Percentage Change\u003Cbr>Here are the two formulas you will need discovering the percentage changes: |  |  |  |  |\n| --- | --- | --- | --- | --- |\n| % Increase = | 􀯇􀯘􀯪 􀯇􀯨􀯠􀯕􀯘􀯥−􀯈􀯥􀯜􀯚􀯜􀯡􀯔􀯟 􀯇􀯨􀯠􀯕􀯘􀯥􀯈􀯥􀯜􀯚􀯜􀯡􀯔􀯟 􀯇􀯨􀯠􀯕􀯘􀯥 |  | x 100 |  |\n| % Decrease = |  | 􀯈􀯥􀯜􀯚􀯜􀯡􀯔􀯟 􀯇􀯨􀯠􀯕􀯘􀯥−􀯇􀯘􀯪 􀯇􀯨􀯠􀯕􀯘􀯥\u003Cbr>􀯈􀯥􀯜􀯚􀯜􀯡􀯔􀯟 􀯇􀯨􀯠􀯕􀯘􀯥 |  | x 100 |\n| As you can see the two formulas are similar – Interestingly, if we use the increase percentage change formula above and the answer is a negative number, then this tells us that it is in fact a percentage decrease!\u003Cbr>So, if you are unsure about anything, use the first formula and it will help tell you whether the change is an increase or a decrease.\u003Cbr>Let’s look at two example questions and you can see both formulasin action (and hopefully you can see which one we would need from the question title) .\u003Cbr>Q: Sales have risen from 130 to 160 in 6 months . What is the percentage change in sales over the 6 months?\u003Cbr>We can see that the change is an increase so we will use the first formula   |  |  |  |  |\n\n% Increase = ~~ ~~160−113030 x 100  \n= 0.2307… x 100 = 23.1%  \nTo double check your answer, take the original number and multiple it by 1 + the percentage increase e.g. 1.231.  \n130 x 1.231 = 160.0… as this is the new sales number, we know weare correct.  \nIf we reverse the previous question, we can try the decrease percentage change formula…  \nQ: Sales have fallen from 160 to 130 in 6 months . What is the percentage change?  \n% Decrease = ~~ ~~130−116060 x 100  \n= -0.1875… x 100 = -18.75%  \nPercentage Increase and Decrease  \nTo work out the new value of something after a percentage increase/decrease there is a simple calculation to follow.  \nFor a Percentage Increase:  \nNew Value = ( 1 + Increase ) x Original Amount  \nAnd for a Percentage Decrease:  \nNew Value = ( 1-Decrease ) x Original Amount  \n| The increase and decrease values are worked out where 1 is 100% . Therefore, with a 30% change, the value we would use is 0.3.\u003Cbr>You can see this in the following example:\u003Cbr>Q: This month's sales increased 25% from last month's 400 sales . How many sales were there this month?\u003Cbr>As the increase is 25%, this will become 0.25 in our formula.\u003Cbr>New Value = ( 1 + 0.25","cbCaigiHOYqY9hlU","https://ap.wps.com/l/cbCaigiHOYqY9hlU","pdf",2254822,"English","# Averages\n## Mean and average calculation\n## Weighted averages\n# Percentages\n## Percentage change: increase and decrease\n## New value after increase/decrease\n## Reverse percentages (original value)\n# Ratios\n## Y:Z ratio with total items","[{\"question\":\"How do you calculate a standard average (mean) from a set of values?\",\"answer\":\"Add all values in the dataset and divide by the number of values. The mean represents the dataset total per item.\"},{\"question\":\"Why can’t you average two percentages by taking the simple middle value?\",\"answer\":\"When combining results, weighting matters because each average may represent a different number of values. You must weight by how many items each average covers (e.g., 15 vs 5 children).\"},{\"question\":\"How do you use a ratio like Y:Z to find the number of each part from a total?\",\"answer\":\"Compute Number of Y = (Y ÷ (Y + Z)) × Total items. With a 7:3 ratio and total 80, this yields 56 for the Y part.\"}]","Numerical Reasoning Formula Sheet - Averages, Percentages, Ratios | PDF",1790970446,23]