Awesome Quantity

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Imaginary Numbers Are Real [Part 1: Introduction]

الأعداد التخيلية حقيقة ,لنقل ان لدينا دالة في متغير (x)، حيث f(x) = x^2 +1.,يمكننا التعبير عن الدالة بيانياً بـ"القطع المكافئ".,الآن لنجرب أن نحسب قيم (x) التي تشكل حلاً للمعادلة,او ما يسمى بـ"جذور الدالة".,بيانياً، الجذور هي نقاط تقاطع الدالة مع محور (x).,كما هو واضح، القطع المكافيء لا يتقاطع أبداً مع محور (x)،,طبقاً للرسم البياني، لا يوجد حل لمعادلة: x^2 +1=0.,لكن هناك مشكلةً صغيرة.,قبل ما يقارب مئتي عام، أثبت رجل ذكي يدعى (جاوس)،,أن كل معادلة كثيرة الحدود من الدرجة (n)،,لها بالضبط عدد (n) من الجذور.,بالعودة لمعادلتنا، فإن أكبر أس أو درجة للمعادلة هو (2)،,لذا، فيجب أن يكون لها جذرين.,واكتشاف (جاوس) ليس مجرد قاعدة عشوائية،,اليوم نسميه (نظرية الجبر الأساسية).,إذاً، فرسمنا البياني يبدو متعارضاً مع هذه النظرية الهامة،,مما يمثل مشكلة.,ما يخبرنا به (جاوس) ، أن هناك قيمتان مثاليتان للمتغير (x)،,بالتعويض بهما في الدالة، سيكون الناتج صفر.,أين يمكن أن يكون هذان الجذران؟,الأجابة المختصرة هي، أننا ليس لدينا ما يكفي من الأعداد.,عادةً ما نفكر أن الأعداد متراصة على مسار أحادي البعد، أو ما نسميه (خط الأعداد).,كل مانعرفه هنا: صفر، واحد،,الأرقام السالبة، الكسور، حتى الأرقام اللا منطقية مثل الجذر التربيعي لـ2.,لكن هذا النظام ليس مكتمل.,و أرقامنا المفقودة ليست في مكان ما يميناً أو يساراً،,أرقامنا في بُعدٍ أخر تماماً.,جبرياً، هذا البعد الأخر,له علاقة وثيقة بمعضلة كانت مستحيلة رياضياً طيلة ألفي عام:,الجذر التربيعي لـ(1-).,عندما ندخل البعد الجديد في تحليلنا،,قطعنا المكافيء يصبح أكثر إثارة.,الأن وقد أصبحت الأعداد في شكل ثاني الأبعاد،,يمكننا رؤية كيف تُمثل فعلاً دالة (f(x,و كيف أن لها فعلاً جذرين بالضبط.,لكننا كنا فقط ننظر للبعد الخاطئ.,إذاً، ما السبب في أن هذا البعد الإضافي لا نعرفه عادةً؟,جزءٌ من السبب، أنه قد أُطلق عليه اسمٌ مريعٌ.,اسمٌ يوحي أن الأعداد التي تقع فيه لا يمكن أن تكون حقيقة.,في الحقيقة، (جاوس) نفسه كان له رأياً خاصاً في هذه التسمية التقليدية:,"الأعداد التخيلية كانت وما زالت مُحاطة بالغموض. يرجع هذا -بحد كبير- إلى سوء تسميتها..,.. على سبيل المثال، لو أن الأعداد (1+) و(1-) والجذر التربيعي لـ (1-) سُميّت: مباشر وعكسي وجانبي (على الترتيب) بدلاً من موجب وسالب وتخيلي، لاختفى هذا الغموض تماماً",.. على سبيل المثال، لو أن الأعداد (1+) و(1-) والجذر التربيعي لـ (1-) سُميّت: مباشر وعكسي وجانبي (على الترتيب) بدلاً من موجب وسالب وتخيلي، لاختفى هذا الغموض تماماً",.. على سبيل المثال، لو أن الأعداد (1+) و(1-) والجذر التربيعي لـ (1-) سُميّت: مباشر وعكسي وجانبي (على الترتيب) بدلاً من موجب وسالب وتخيلي، لاختفى هذا الغموض تماماً",وهكذا، هذا البعد المفقود يتكون من أعداد أُطلق عليها اسمٌ سخيفٌ وهو "الأعداد التخيلية".,اقترح (جاوس) تسمية هذه الأعداد بـ(الأعداد الجانبية).,اذاً من الأن فصاعداً، دعونا نستبدل (التخيلية) بالـ(الجانبية),لفهم الأعداد (التخيلية) بشكل أفضل,أعني (الجانبية),واستيعاب ما يحدث فعلا،,دعونا نتفكر قليلاً في الأعداد عموماً.,البشر قديماً لم يستخدموا إلا (الأعداد الطبيعية)، 1 و2 و3 وهكذا.,هذا منطقي طبقاً للهدف الذي كانت من أجله تُستخدم هذه الأعداد.,اذاً بالنسبة لهم كانت الأعداد عبارة عن سلسلة من النقاط.,بتقدم الحضارات،,احتاج البشر إجابة لأسئلة رياضية أكثر تعقيداً،,كموعد زراعة البذور مثلاً،,أو كيفية تقسيم الأرض، أو كيفية متابعة التعاملات المالية.,الأعداد الطبيعية ل

The above is a brief introduction to Awesome Quantity

Let's move on to the first section of Awesome Quantity

Quality vs Quantity | Ridiculously Awesome! - #1 | Pastor John Lindell

well tonight we're going to start a,four-week series and it's a series that,we've entitled ridiculously awesome,faith and so the idea is simply to,remind us should I think it's good for,us every now and then to just make sure,we're we're dialed in on the things that,really really matter day by day,and faith is is honestly one of the most,important because the Bible says without,faith it is impossible to please God,because anyone who comes to him must,believe that it exists and that he,rewards those who earnestly seek Him so,one of the things I pray regularly as,Lord increased my face strengthened my,faith helped me to walk by faith to,believe you for great things and so what,we're doing is tonight we're going to,just kind of introduce the whole idea of,faith and we're going to be looking in,the next few weeks about people who,believe God for some pretty big things,now here's the good news about faith as,important as faith is I mean if you,can't receive from God please God walk,with God without faith then you know,it's really important but here's the,good news about faith it doesn't take a,bunch doesn't take a lot of faith I mean,all you have to do is act on the faith,that God gives you be open to receiving,it act on it,exercise it like a muscle watch it grow,but honestly tonight as we talk about,faith as it relates to quality and,quantity the quality of faith is more,important than the quantity of faith and,it doesn't take a whole bunch of faith I,mean even if you have think of this even,if you have like a monster problem a,ginormous problem faith as small as a,mustard seed is enough to receive from,God which I don't know about you is very,very encouraging,on three different occasions apparently,this was a principal Jesus liked to talk,about,and on three different occasions so we,know this is a part of his ministry it,was an illustration that he used,frequently to help people grasp faith,but on three different occasions he,spoke about the power of a faith filled,statement the power of giving voice to,faith in our words and use the,illustration of moving something twice,of of up rooting it and moving it into,the sea and once just simply moving it,let's look at it Matthew chapter 17 I'll,bring him up he said to them because of,your little face so the disciples had,come to him and said why couldn't we,heal the boy or cast the demon out of,the boy mark says cast the demon out,Matthew says healed,jesus said to them because of your,little faith for truly I say to you if,you have faith like a grain of mustard,seed just a tiny speck of faith you will,say to this mountain move from here to,there and it will move and nothing will,be impossible for you as Jesus is saying,this he's saying it in the shadow of the,largest mountain in the region of,Galilee in the Land of Israel it is,Mount Hermon and so he's saying listen,if you had the faith as small as a grain,of mustard seed you could say to this,gigantic mountain move from here to,there and it would do it a

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Awesome Number Counters 💯 | Exciting Scratch Game & How to Tutorials

hello fellow scratchers have you made a,great scratch game but felt it was let,down by using scratch's built-in,variables for the score or timer,yeah we've all been there well worry no,more because today i will be showing you,how we can dispense with those and,replace them with something a lot more,awesome oh yeah come on the concept is,pretty straightforward we need to have,the digits 0 through 9 as costumes of,our sprite and then we add a little code,in to handle the rest and that's what,i'm here for so guys without delay,let's get scratching,we'll begin with a fresh new project and,quickly mock up a simple clicker game we,just need a score variable for all,sprites,there it is,and then when this sprite is clicked,we change score by,one wow,this is about as basic as it gets right,we click our cat and the score increases,job done,but gosh it would all look so much,better without this boring generic,variable reporter it's so small and,uninspiring i mean we could double-click,the score on the stage to change how it,looks that's a tad better but it hardly,adds to the excitement of me clicking,the cat,no what we really want is for the score,to be large colorful in your face and,really funky the only way we can,currently do this is by using sprite,costumes,well alrighty then we'll start by making,a new sprite,i'm giving mine the name score,click to choose a new costume from,scratch's library and search for glow,now you notice there's a whole costume,font already made for us well that's,handy choose the zero digit first,so that looks pretty cool much more,exciting than a variable reporter,now we need to import the other nine,digits one costume at a time i've copied,the word glow into my clipboard so that,i can paste it into the search box and,save time,however don't feel you are stuck using,this particular font the tutorial will,work just fine if you want to draw your,own,that would be super fun and would make,your project unique to you,phew i've imported all 10 costumes 0,through 9.,let's center the costume on the stage,just move the score variable reporter,out of the way first,yeah that looks great now we just need,to figure out how to make the beautiful,new digit display the same number shown,in the variable reporter,often a problem is not so hard to solve,if you can first break it up into,smaller problems and then solve these,smaller problems one at a time,rather than tackling the whole score of,117 then we'll begin by looking at just,the first digit the character one,come into the code tab of our score,sprite,let's start by setting up our sprite,when green flag clicked go to x y,the current position of the score sprite,is pre-populated for us great,to help explain what we are doing i'll,bring in a say block from the looks,category and for now simply say the,value of the variable score,hit the green flag to run the project,and we'll see the full score of 117,displayed,but for now we only want to deal with,the first digit of this longer number,lucki

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The Map of Mathematics

Matematika që mësojmë në shkollë nuk i bën drejtësi mjaftueshëm fushës së matematikës.,Ne shohim vetëm një kënd të saj, por matematika si tërësi është lëndë e madhe dhe,me një llojllojshmëri të mahnitshme.,Qëllimi im me këtë video është të ju tregoj juve të gjitha ato gjëra mahnitëse.,Ne do të fillojmë që nga më e para pikë e fillimit.,Origjina e matematikës bazohet në numërim.,Në fakt, numërimi nuk është vetëm aftësi e njeriut, kafshë të tjera kanë aftësi të numërojnë gjithashtu dhe,dëshmi për numërimin e njeriut shohim që në kohët pre-historike me shenja të bëra në,eshtra.,Përgjatë viteve ka pasur risi të ndryshme, me ekuacionin e parë nga Egjiptianët,,Grekët e lashtë bënë hapa të mëdha në shumë fusha si gjeometria dhe numerologjia, dhe numrat,negativ ishin zbuluar në Kinë.,Dhe zeroja si një numër ishte përdorur për herë të parë në Indi.,Pastaj në Kohën e Artë të Islamit matematicientët Persian bënë hapa të mëdha mëtutje me librin e parë,të shkruar për algjebër.,Pastaj matematika lulëzoj në renesancë përgjatë shkencave të tjera.,Tani, ka më shumë për historinë e matematikës se sa ajo çka unë sapo thashë, por,do të kërcej në kohën moderne dhe matematikën ashtu si ne e njohim.,Matematika moderne për së gjeri mund të ndahet në dy fusha, matematika e pastër: shkenca,e matematikës për hir të vetes, dhe matematika e aplikuar: kur ju zhvilloni matematikën në ndihmë,të zgjidhjes së disa problemeve reale në botë.,Por, ka shumë mbikalime.,Në fakt, shumë herë në histori dikush ka kaluar përgjatë shkretisë së matematikës,motivuar thjesht nga kurioziteti dhe sikur i drejtuar nga një sens estetik.,Dhe pastaj ata kanë krijuar një tërësi të re të matematikës që ishte e mire dhe interesante,por nuk sjell diçka që mund të jetë e dobishme.,Por pastaj, le të themi pas qindra vjetësh, dikush do të punoj në ndonjë problem në këndin,e fundit të fizikës apo shkencës kompjuterike dhe do të zbulojnë që kjo teori e vjetër në matematikën e pastër,është pikërisht ajo çka ju nevojitet për të zgjidhur problemin e tyre real të botës!,Që është e mahnitshme, mendoj!,Dhe kjo lloj gjëje ka ndodhur kaq shumë herë përgjatë shekujve të fundit.,Është interesante sa shpesh diçka kaq abstrakte përfundon të jetë shumë e dobishme.,Por do duhej të përmendja dhe se matematika e pastër në vetvete është ende një gjë shumë me vlerë,për tu bërë ngase mund të jetë interesante dhe në vetvete të ketë bukuri dhe elegancë të vërtetë,që gati bëhet si art.,Në rregull mjaft me këtë shpjegim të entuziazmuar, le ti hyjmë punës.,Matematika e pastër është e përbërë nga disa pjesë.,Studimi i numrave fillon me numrat natyral dhe çfarë mund të bësh me ata me,operacione aritmetike.,Dhe pastaj shikon lloj të tjerë të numrave si numrat e plotë, që përmbajnë numrat negativ,,numrat racional me thyesa, numrat real që përfshijnë numrat si pi që vazhdojnë në,pika të pafundme decimale, dhe pastaj numrat kompleks dhe një tërësi tjetër.,Disa numra kanë veti interesante sikur janë numrat e thjeshtë, ose numri pi ose eks

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EP 174 - Lucknow Biriyani, Tunday Kababi & Chikankari Kurti, ഇവിടെ എല്ലാം കിട്ടും, Lucknow Food Tour

A cold morning at Uttar Pradesh ,It is 17-18 deg C, but very cold in the morning ,We are going to have Lucknow biriyani and explore Lucknow food today ,Lucknow is a food paradise. You get varieties of food here. ,Welcome to a new video of Tech Travel Eat ,We are now at Faizabad road ,This is like going through MG road Ernakulam,Lucknow metro is what you see above us ,All the places in Lucknow have 4 lane roads, they are neat and impressive ,We dont know how it is going to be further down ,We are going to old Lucknow side now ,We are at New Lucknow side now. ,The buses here are rusted. ,I think this is like Connaught place, Delhi.,Lot of multi branded store on both sides.,You have PVR too.,Its a happening street and best to visit in the evenings.,Meena bazaar, an old Kapoor hotel, Divisional railway manager office ,I this is an underground metro place.,The metro has come out from here ,Parking space at the biriyani place is narrow. ,So we have parked close to a park ,We shall catch an auto and go to have biriyani,We have a bro coming. Lets ask him ,This is e rickshaw,Look at Rishi holding and sitting,Good we didnt take our car this side. The roads are very narrow,Most of the food streets are at a narrow street,But they are awesome ,Full block. How about getting down here? ,Somehow we managed to come here. Or will not have come ,A crowded street ,He is frying chicken there ,We have come to Tunday Kabab to have food ,Can we sit and have?,Let me find out. They do have I guess. ,They have so many things here. I think this is biriyani,Preparing kababs live ,Ask them to show that biriyani ,This is their menu card ,Tunday Buffalo kabab is their most famous item,You get only that in UP,You should buy the first one ,That is famous here ,What is the man at the end there making?,Abhi will have mutton. Let us go inside and order. ,He is making rumali roti there ,That is then kept here ,This is another roti. Why is it red in colour?,This is Mughlai paratha ,They have a lot of rotis here ,You have varieties of rotis ,That is the specialty here ,Thats what confuses us. What he making?,Mughlai paratha ,What are they adding to this?,Shirmal. I havent had it so far. ,Lets try it out. ,Here everything is set to grill chicken. Those grilled are kept there,Is this chicken biriyani?,Let us go inside, sit and eat. You have the photos of celebrities who came here ,I guess all have come here ,A long list and photos of the celebrities who have visited this place ,It is full here. ,It is like people waiting at wedding food places. ,People standing in queue,Finally we got a seat. Its very crowded. ,They came and took order after 10-15mts ,This place is worth. All do come and give it a try. ,This hotel has been running since years ,It is very famous ,You saw the photos displayed downstairs. You can guess how good it is ,All of you should come ,It is not the kind of kababs you get everywhere ,You have to come here and eat to know the difference ,He has begun showing expression

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IF FOOD WERE PEOPLE || Awesome Situations by 123 GO!

What? You’re not gonna share your snacks?,Nope! They’re all mine!,Weeee! That was fun. But now to get comfy.,Hey. Hey! Are you okay?! Spit it out!,Knock it off! I’m nice and cozy in here.,Argh! I said stop!,Oh no! Looks like I’m being evicted!,Phew. That was a close one.,I’ve worked so hard to be here!,Oh! My diploma!,Mom! Look! I did it!,I see you, darling! I’m so proud!,Wait. What is that…? Lily, in your teeth.,Huh?,Yay! It’s me! Lettuce! Thanks for all your support!,In your teeth!,Oh! Oh nooooo!,Ahh! How embarrassing!,Uhh, excuse me. This is my limelight.,Ow. Go away!,Ooh! No more photos!,That’s right. I’m here to stay! ,Ooh, these smell great!,Perfect! Cupcake masterpieces!,Hey, do you smell something?,No way! Look at these cupcakes!,Let’s dig in!,Oh wow. Those were sooooo good.,One left? It’s mine.,No way! It belongs to me!,Give it!,No, you give it!,Ahhhh! They’re fighting over me!,Hey! This is pretty fun, actually!,What the…? My cupcakes!,HEY! Give that to me!,How dare you? This is MY cupcake!,Great. You happy? Neither one of us got it.,It was your fault.,These chopped carrots are gonna taste great.,Now for the broccoli.,Now for the oil.,The oil is really gonna take this to the next level.,Can’t forget to season these veggies.,In you go! It’s roasting time!,Okay, better set my timer. I don’t want to forget about them.,How relaxing, right?,I know! I’m really enjoying myself today!,Huh. Do you hear that? Like an alarm?,Better check on these veggies.,I’ll just give them a quick stir.,Perfect. Back into the oven they go.,Oh, I guess we’re supposed to turn over.,There we go. ,Cheers! ,Mm. The salad is excellent!,Ooh, looks at those whole cloves of garlic.,No one’s around. I’ll just take a quick bite.,You know what? I’ll just eat the whole thing!,It tastes soooo good!,Oh no! My breath!,Hi! Umm, I said hi!,Hi.,Oh! Oof. Girl, your garlic breath is harsh!,Give me one second. Look, here’s some gum.,Believe me, you need it.,Thanks so much.,Oh, it’s terrible in here!,Good thing I can freshen things up.,Yuck. She must’ve been eating a ton of garlic.,Wait a second…,What the heck is that? Who dares?!,Hey! You! What are you doing here?,I was invited here.,Everyone loves garlic. You need to leave.,Everyone might love garlic but no one loves garlic breath.,Aroma police? NOOOO!,I don’t want to go to jail!,Hey, garlic! Welcome to the cell!,But it’s not fair!,Hey. Don’t eat any more garlic.,Woo! This party is great!,I love this song! I’m dancing all night long!,Oof. I am not ready for school.,She’s not looking. I can sneak in.,I’m so tired. Good thing I’ve got this coffee.,Oof. It’s not really helping.,How are you doing?,Because it’s time to WAKE UP!,You’ve got too much to do to be sleeping!,Hmm? Where’s she running to?,That’s right! Diagram those molecules!,What’s she doing over there?,Is she… solving equations?,Keep going! Never stop!,Now she’s dusting?,That’s right! Show this chemistry lab who’s boss!,Oh. Ohhhhh… my coffee has worn off.,I could really go for

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INSANE Amounts of Games Coming to STEAM and AWESOME Game Finally Comes to PC!

yo what's going on guys mush back at it,with another video got a couple of,things to talk about in this video,wanna talk about the number of games,that have been coming to steam,especially in 2017 we're talking just,pure numbers in this video and then,we've also got confirmation of a cult,classic an absolutely terrific game,finally coming to PC later this year,more on that in a little bit first let's,talk about the enormous amount of games,that have been coming to steam in 2017,if you guys have been gaming on PC and,following game releases on Steam you,guys know that there are a ton of new,games every week even every day we're,talking on some days you see upwards of,10 games released in a single day in a,week sometimes it tops over 50 games and,that's just a crazy amount of games a,lot of these games are shovelware,they're definitely not the biggest games,in the world but every week you tend to,find 3 or 5 gems that you can add to,your wishlist and you can check out when,they do go on sale however a lot of,these games do really go under look I,mean when you have an enormous number of,games releasing it's just hard for,Steven valve to allocate a proper amount,of marketing for each games you see,marketing catered towards different,users depending on what games they play,and whatnot and I think that's a good,idea,but still given the quantity of games,that have been coming on Steam it's just,absolutely crazy and an actual number is,that over a thousand games have been,released on Steam since Steam direct was,introduced back in June that's about two,months and change a thousand games in,that time period is absolutely crazy and,2017 up until this point in September,has already released more games than,were released in the entirety of 2015,and if you look at steam game releases,from 2006 to 2014 you combine that all,up 2017 has add more game releases than,that entire cumulative time period I,mean I hope you guys understand how,absolutely freaking crazy that is how,quickly steam has grown in just the last,few years now 2016 was a mega year - but,2017 is on track to beat that handily,and that's just crazy let me know what,you guys think in the comments section,down below do you like that there's so,many games on Steam or for you is it,more of you finding the games that,you're interested in those big games,like the pub G's of the world are,obviously gonna be huge but then for,every pub G you know there's a thousand,fifteen hundred games that just go,completely underlooked,yes pub G is an enormous,successful game and kudos to the,developers on that it's great that,they're making a ton of money it's great,that a lot of money is being put into PC,games through pub G but then you've got,all those other games that really are,getting no attention whatsoever and,maybe deservedly so maybe they aren't,the best games in the world but they're,still releasing on Steam and I don't,know for me I do like it but I do know,that a lot of people just think steams,marketplace

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Tenchukunte Tegipotunda Video Song | Preyasi Raave Movie | Srikanth | Raasi | Suresh Productions

Preyasi Raave Heart touching Scene

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10 Awesome Channels - Quality Over Quantity

there are some youtube channels that you,can watch every day their content is,entertaining but also simple enough that,they can upload many times a week but,then there are the channels that you,forget that you even subscribe to them,but then as soon as they release a video,you stop what you're doing and you watch,it all the way through so today i put,together a list of top 10 highest,quality youtube channels,you know channels that are the opposite,of mine now to be honest i put this list,together thinking,all right this is a great list i've got,the top 10 channels on youtube,and then i've decided to make a post for,you guys to comment on what channels you,think are the highest quality,and you gave me tons and tons of,suggestions and i've been watching a lot,of them,and so rather than me going crazy trying,to rank every single channel on youtube,i'm just going to turn this into a,weekly series where we look at 10,awesome underrated channels so feel free,to throw all your favorite channels in,the comments and i'll check them out,but for now here is my top 10 list of,channels that put a ton of work into,every video,starting with number 10 the hoax hotel,now the hoax hotel is probably one of,the funniest channels i've ever seen on,youtube,the whole premise of the channel is he,likes to find scammers that he can call,and just kind of mess with and waste,their time these scammers often live,somewhere in india or,africa and as a result have pretty,broken english and so what the hoax,hotel does is that he calls these,scammers,and he likes to just kind of play dumb,just being as annoying as possible while,trying not to get hung up on,now the challenge with this is that you,have to act stupid enough,that they feel like they can still take,advantage of you,but you can't act so stupid that they,realize that you're messing with them,so there's a really golden middle ground,that you have to stay in,but as far as the video quality goes he,actually puts a lot of effort into,basically animating all of the videos i,don't know where he gets all these,images or how he does all of the art for,this channel but it really adds to the,entertainment value,if you want to receive,oh in us dollars that's what i'll be,uh purchasing the flight in,and it's just so funny to listen to the,reactions of these people on to number,nine,and that is the killian experience now,when i said the hoax hotel is one of the,funniest channels i've ever seen on,youtube,killian experience is one of the very,few that can actually top that,you have to remember united states at,the time like they had landed on the,moon,but they were still years away from,creating halo so it was still considered,like a,like a niche country now with this,channel a swedish guy with a very dry,sense of humor,puts very creative commentary on,whatever the subject is,some of his best videos include a,garbage retrospective to lord of the,rings,to the star wars prequels or to harry,potter,and for anyone who's fans of these,f

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Doing it the right - Weighted averages in Excel (introduction to awesome SUMPRODUCT)

hello and welcome to shizer org in this,video we are going to look at how to,calculate weighted averages in Excel now,when you try to calculate a weighted,average in Excel you will quickly,realize that there is no weighted,average function or formula available we,can calculate average we can calculate,average ifs we can calculate a median,and whatnot,but not weighted averages so how would,you go about it well there are a couple,of sneaky little tricks that you can,apply to calculate weighted averages and,one of them is my favorite it is to use,some product formula so without further,ado let me get show you how to do this,in Excel so we got some data here with,various product types and what is the,quantity per customer that we have let's,say smartphones 1.8 quantity sold per,customer for some business laptops 1.23,and video games 4.9 at the overall,business level if I want to find out,what is my business,average quantity per customer we could,call this as Q PC and this would be the,wrong way to go about it right if I,simply say average of all of these,numbers I would get some sort of a,rubbish number like two point five two,one six six seven now remember this is,wrong you should we are not supposed to,be doing average of averages the correct,to be to calculate this would be to use,more information because we don't know,how many customers we have in each of,those product categories we are not able,to tell you what is the overall business,weighted average of the quantity per,customers but if we want to have that,information like if we know how many,customers we have hope we can calculate,this given the number of customers each,of those products have we can calculate,County which would be customer times,quantity,customer and that's my quantity and then,I can calculate qpc I'll call this as,version one this is the correct way to,do about this which is sum of quantity,divided by sum of customers and that,would be two point three one right but,this requires us to add an extra column,and this column all it is doing is,multiplying these two numbers putting it,there and then what we are using is we,are not even using that column directly,we are using a sum of that column its,sum of all those multiplications that's,out Excel has a function that does the,some of those multiplications it's,called some product what some product,does is it takes two sets of numbers,this number and then that members and,then it can give me the entire sum of,all those individual multiplications the,key criteria here should be that both of,them should be of same size right if,this has six numbers that should also,have six numbers as long as that is true,Excel can give me multiplication of,those two you can provide multiple lists,as well not just two but in this case we,only need two so our total quantity,comes up to be 134 thousand point 134,thousand one and then I just need to,divide this with my total customers and,we get weighted average here that's the,weighted average of all

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