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The content further presents short solution-style question prompts referencing CAT 2020 and CAT 2021, covering average speed, arithmetic mean of scores, middle-term properties, and multi-variable age and job-salary average setups, with options and calls to watch video solutions via provided links.",{"@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":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/quant-formula-book-by-quantifiers-cat-academy/347407/",{"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/quant-formula-book-by-quantifiers-cat-academy/347407.png","ImageObject",300,407,{"name":92,"@type":93},"Ophelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-22",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the document define as “average” (arithmetic mean)?","Question",{"text":112,"@type":113},"It defines average as the arithmetic mean of the items. It also explains that when the terms are in equal difference order, the middle term(s) represent the average depending on whether the number of terms is odd or even.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does average change if the same value is added or subtracted to every item?",{"text":117,"@type":113},"If x is added to all items, the average increases by x; if x is subtracted from all items, the average decreases by x.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the concept of weighted average mentioned in the material?",{"text":121,"@type":113},"The document includes a weighted average section with a formula reference, indicating that the average depends on weights associated with each value.","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},347407,1790471316,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","|  |  |\n| --- | --- |\n| |  |\n| Get Daily Targets on your WhatsAppor Copy paste this URL: [https://forms.gle/oSih8jQCermJq71q9](https://forms.gle/oSih8jQCermJq71q9) |  |\n\n\n|  |  |\n| --- | --- |\n| |  |\n| Get Daily Targets on your WhatsAppor Copy paste this URL: [https://forms.gle/oSih8jQCermJq71q9](https://forms.gle/oSih8jQCermJq71q9) |  |\n\nCopy paste the link to watch the video before you begin the next topic  \n[https://youtu.be/8Bkl7prrRQc](https://youtu.be/8Bkl7prrRQc)  \nJoin our WhatsApp FREE 24/7 Doubt Solving Group (if group is full, follow us on Instagram  \n@quantifiers_cat for the new link)  \nClick here to join WhatsApp group  \n[https://chat.whatsapp.com/EX8fGeD7h0zAhs9sDa5eeA](https://chat.whatsapp.com/EX8fGeD7h0zAhs9sDa5eeA)  \n\n| About Quantifiers CAT Academy |  |  |\n| --- | --- | --- |\n|  | Quantifiers started online in 2019 and within a short period of time, it achieved what many renowned Institutes dreamed of, producing 28, 99+ %ilers out of the total~275 students taught, Quantifiers revolutionized the teaching industry. Quantifiers is best known for their pedagogy, their emphatic attitude towards every single student and for the passion with which every single element is driven\u003Cbr>Managed by the three musketeers Rohit Kanwar, Sahil Arora & Jasneet Dua, Quantifiers is one of the most well managed CAT preparation player in India, it has helped more than 1 lakh aspirants achieve their dreams through their teachings.\u003Cbr>Be the part of legacy, join Quantifiers at [www.quantifiers.in](www.quantifiers.in) |  |\n|  |  |  |\n\nCopy paste the link to watch the video before you begin the next  \ntopic  \n[https://youtu.be/f7RH9Jjd4rg](https://youtu.be/f7RH9Jjd4rg)  \nJoin our WhatsApp FREE 24/7 Doubt Solving Group (if group is full, follow us on Instagram  \n@quantifiers_cat for the new link)  \nClick here to join WhatsApp group  \n[https://chat.whatsapp.com/EX8fGeD7h0zAhs9sDa5eeA](https://chat.whatsapp.com/EX8fGeD7h0zAhs9sDa5eeA)  \nArithmetic  \nAverage  \nAverage means Arithmetic mean of the items and it is = NSumumbeorfIotfemsItems  \nWhen the difference between the terms is same and the total number of terms are odd (sayn), then the middle term = (n + 1)/2th term is the average of all the terms.  \nWhen the difference between the terms is same and the total number of terms are even (sayn), then n/2 and n/2 + 1 are the two middle terms and the average of all the terms is equal to the average of these two middle terms.  \nAverage speed: If a man covers some journey from A to B at u km/hr. and returns back to A at B uniform speed of v km/hr. , then the average speed during the whole journey is 2􀯨􀯩􀯩 km/hr  \n1. If x is added in all the items, then average increases by x.  \n2. If x is subtracted from all the items, then average decreases by x.  \n3. If every item is multiplied by x, then average also gets multiplied by x.  \n4. If every item is divided by x, then average also gets divided by x.  \n􀯔 1􀯫 1 +􀯔2􀯫2 + .... 􀯔 􀳙􀯫 􀳙  \n5. Weighted average = ~~ ~~  \n􀯔 1 +􀯔2 + ...... +􀯔 􀳙  \n1  \nOnion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to (CAT 2021)  \n26  \n16  \n18  \n20  \nClick here for  \n\n|  |  |  |\n| --- | --- | --- |\n|  |  | video solution |\n|  |  |  |\n| 2 | \u003Cbr>In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is: (CAT 2021) | Click here for |\n|  |  | video solution |\n|  |  |  |\n| 3 | \u003Cbr>The arithmetic mean of scor","cbCaimrOu81bMQBO","https://ap.wps.com/l/cbCaimrOu81bMQBO","pdf",12813025,100,"English","# Arithmetic\n## Average (Arithmetic Mean) - core properties\n## Average Speed - journey-based average\n## Weighted Average - formula reference\n# CAT Practice Questions\n## CAT 2021 - onion expense average\n## CAT 2021 - football goals average\n## CAT 2021 - student score mean and toppers\n## CAT 2020 - age ratio average condition\n## CAT 2020 - batsman innings average and constraints\n## Teacher jobs salary averages - three categories\n## Test scores - maximizing score difference","[{\"question\":\"What does the document define as “average” (arithmetic mean)?\",\"answer\":\"It defines average as the arithmetic mean of the items. It also explains that when the terms are in equal difference order, the middle term(s) represent the average depending on whether the number of terms is odd or even.\"},{\"question\":\"How does average change if the same value is added or subtracted to every item?\",\"answer\":\"If x is added to all items, the average increases by x; if x is subtracted from all items, the average decreases by x.\"},{\"question\":\"What is the concept of weighted average mentioned in the material?\",\"answer\":\"The document includes a weighted average section with a formula reference, indicating that the average depends on weights associated with each value.\"}]","Quant-Formula-Book-by-Quantifiers-CAT-Academy | PDF",1790066803,252]