What is a "Standard Deviation?" and where does that formula come from

Stuck on standard deviation?? This video will help you understand what that crazy formula really says.. Watch a few times if necessary... "THE AVERAGE DISTANCE TO THE MEAN!!" *sort of... How to think of this measure of spread...

[@thegoonist]

his enthusiasm for teaching is infectious. everyone should have a teacher like him.

[@Kennythesamuri]

Its almost like watching a Blue Clues episode about Statistics

[@earthdoesurvivalcraf]

XD ikr

[@gyohza]

Sometimes I stop and wonder what my days would be like if it weren't for KZbin comments

[@lovelyxskinny]

😂😂😂😂

[@punkinhaidmartin]

Σ|ow, Σ|ow, Σ|ow.

[@bioquatic]

..I love this guy!..took me 50 years to finally get back into math, and he just made it fun!

[@wendyv.v.1299]

On hearing the kids in the background (in what I assume is his house): "Oh, thank god, this guy has reproduced." We need more math profs like this! Thanks so much!!!

[@plumSlayer]

funny XD

[@bigboss-wr5hb]

You truly deserve an oscar. Thanks so much for this, you're amazing.

[@fanakissferobolus9767]

great teacher, great actor,indeed:)

[@rubymendez388]

I like how you did this video. We need more people like you. Some professors are just so boring and I feel like I'm falling behind cuz they explain so poorly. But your examples are fun and keep me awake! LOL

[@sasvalue]

+Ruby-J. Mendez True Ruby

[@contrerasjose8078]

Red Stone a

[@dreamdamons4576]

He is quite amazing yeee. U wouldn't believe it but I perform my psychoanalytic presentations like this. Totallyyyy Krazyyyy

[@BuyBBStonk]

how far are you SQUARE IT!

[@biglance]

10 intensive days in an MBA Stats class...and I learned more in 17 minutes here with you Sir...God Bless You!!!!!!!!!!!!!!!

[@AN-ks7vb]

I did not know how fast the 17 minutes went away!!! I could understand and will permanently remember the concepts taught!!! Extraordinary teaching.. You are unique and energetic... keep up this way.. do not change based on some tasteless comments ... you are one of the best teachers who can keep the audience entertained while they learn it really well!

[@demaslumba5855]

Couldn't agree more!

[@thereeves2000]

I wish you were my math teacher. I didn't learn math from my teacher, I could have learned math from you. Amazing performance. D.

[@frankleahy4309]

Same here, I can not understand a thing my BSTAT teacher says because he is Indian and he just reads right from the power points, but I understood this.

[@77legocreator]

This is the best educational video ever. The message was conveyed with comedy but also in a crystal clear manner. Basically amazing. Thank you so much

[@gaylesherwood2214]

Thank you, I found myself in a class where the teacher isn't actually teaching us the math portion, just the terms. this has saved me!!

[@DeepakKumar-bm1ce]

It made sense Sir. Thanx for explaining in a lucid and crystal clear manner.

[@Avofan]

I wish you were my math teacher. I now have better understanding of standard deviation. Thanks!

[@josh18230]

A math teacher with personality and oratory skills? More of those and people would be a lot better at math. Great video!

[@pedrosousa338]

Is personality being a clown?

[@workingstiff19]

pinche pedro: What did you say your contribution to this discussion was?

[@veritas785]

I think he is teaching children and your idea of a clown is what children like. In fact, having a straight face while teaching is the most disengaging way of teaching - even for adults. Did you try teaching children anytime, buddy?

[@strongsecurity7747]

Josh Hunter yep !!!!!

[@pawnstorm17]

so true!! I would have been acing my maths back in the undergrad if I had a prof like this great guy!

[@abeljayel4168]

Hands down - the BEST way I've seen this taught....I was CLUELESS coming onto this video--I'm DEFINITELY test-ready on this now. I paused the video before you worked out the sample problem, tried it on my own and did it right the first time! Awesome instructor!

[@ilia9186]

Thank you MrNystrom, your teaching style is very upbeat and has a great pace. I wish my college professors had half of your talent when it comes to teaching. I'm watching your videos for my business statistics course and I'm really enjoying how you simplify the material. Again, thank you so much and keep up the great work!

[@EM-on7en]

I'm going to watch every video you've posted. This was such a huge help! I love the humor, the energy, the entertainment, and (mostly) the approach to teaching. It's brilliant!

[@Daveyrawrz7]

Dude. I can't thank you enough. Now I know how people feel when I make a tech tutorial for them. This was so clear and awesome. Thank you so freaking much.

[@joshwilliams1747]

Thanks man! I'm an Oral English teacher currently teaching in China and preparing for the GRE and standard deviation has always kicked my butt. I loved your body language crazy enough to keep people's attention and asking the questions that we already have. Perfect teaching style. I'm sure you don't hear it enough (none of us educators do) great job, and great energy. Thank you!!

[@alarusie]

I really like your way of teaching. You break the puzzle into paces, you simplify it, and then you fix it one by one until the whole picture is drawn. Thank you very much.

[@kennethhowell5291]

I love it when you have a teacher that knows what he is talking about. You can learn the concept in about 3 seconds. Thank you very much!

[@Maxquaza]

You my friend are extremely talented at what you do. It's a nice surprise to find a teacher who keeps a lesson interesting and unique. Thank you so much :)

[@brenda.castaneda]

OMGGG I SWEAR THIS IS THE BEST VIDEO I SEEN YOU KEPT IT SO ENTERTAINING AND FUN WAY THE WAY YOU EXPLAIN IT *CHEF KISS* you made so easy to understand

[@sussy0506]

You are the BEST math teacher I have ever seing before. Your videos are now the only source I will reach out for help. Thanks for your passion that it's contentious to everyone who listens to you.

[@Skull12o12]

I miss when math was this easy. I wish my engineering professors were this elaborate and entertaining.

[@alldsiupdates]

Are you taking an Calculus-based engineering stat course?

[@Skull12o12]

Supreme Gentleman no sir. never have taken stat.

[@alldsiupdates]

I see. I'm an EE major and I have to take a class like that this upcoming semester. I thought that you were taking something like it and this was being discussed in your class.

[@Skull12o12]

Supreme Gentleman No I actually just randomly was wondering one day what people meant by standard deviation and youtubed it. I learned it in middle school with the mean median mode stuff but never understood it. and nice dude I'm a mech-e.

[@gmpgreen]

Haha, I hear ya. In 1st year engineering right now

[@DenisG631]

This is how the concepts should been explained! Thank you, sir, for the awesome work you've done!

[@yasirarabzai284]

Wow, I used to find music, movie and all the entertaining stuff exciting on KZbin but after watching this video not only taught me the lesson but made me realize that even Maths can be interesting. Thank you, Keep the great work up.

[@isky333]

You are amazing! I went through like 4-5 different websites before I landed here on you tube and you literally "Nailed" it in my "understanding". It's like a permanent folder being created on my Brain Drive that I would always be able to refer to whenever I see this word "Standard Deviation". It is the first video of yours that I have seen and your abilities and style forced me to subscribe to your channel - I don't even know your name but will get to see it after I am done with the comments here as I so much want to appreciate your efforts and style. Kudos man, you rock and may God bless you!

[@malevip]

I swear i will never forget what variance and standrad deviation is for my life!! This video is that good! Your teaching is just out of this world!

[@victoriabarbaros8788]

I fell in love with this teacher :D I love the passion with which you explain this topic to the viewers! I understood it better :3 Thank you!

[@gi5089]

What an absolute hero. Took me like so long to understand it. About halfway through this video I got it immediatly. Thank you so much. Keep doin' what your doin'

[@Bm23CC]

3 years ago I had my statistics exam and I hadn't studied anything. I got up a few hours before the exam and searched you tube and found this video and channel. I got an honour in my exam and I was thrilled. All thanks to this man. Thank you.

[@ehsanhabibi5587]

I really learned something from it! I was confused with many obscured tutorial available online! but Salute to you man! good job

[@GideonGardens]

Best explanation I've ever heard. Thanks:)

[@fotyfar]

Very goid, first time I understand it /)

[@fotyfar]

Best one

[@josephawni]

dude, this is just perfect!!!!!!!!!!! I watched many many videos, but no one was even close to answer the question marks that I had... it's like you are reading my mind...

[@andreajung7885]

oh my gosh. this is so fantastic! not only did I make fully understand but also I fully focused on the contents while watching. Thank you!

[@silversk8erz]

Looks like bruce banner from avengers lol

[@Theonegamefreak]

ty houge The secret is, he's always angry.

[@TheAbeSystem]

+ty houge I was like i've seen him somewhere lol

[@monsterjazzlicks]

More like a Gym Instructor!

[@scwalcofscwalcof1404]

I read that as "averagers" which actually a bit more fitting

[@amazingkris]

Look up "Because Science" on KZbin, and you'll find Thor teaching physics and dynamics.

[@Blubberwagon]

Energetic and well taught! Thanks for the lesson, and keep on teaching!

[@stacyhansen8017]

I so love you. You are the first person to make this understandable for me. Thank you!

[@Mouthymensch]

THANK YOU !! YOU ARE A LIFE SAVER!!! when my professor was explaining this in class it went over my head. I like how you broke everything down and explained what the formula means and what all the symbols mean.. so thank you!!!!

[@adamzerner5208]

I love how you take us through the reasoning process behind how the formula was created!

[@ccbgaming6994]

What reasoning? It's just a dissatisfying approximation

[@olilovesonedirection]

he is sooooo gooooood i had no freaking idea what this was in class (i have a test tomorrow) and this helped me so muuch thank youuu!!!!!

[@bailoutrishi6798]

I got this video to watch and take notes on over the summer, and you've done an amazing job explaining it in full detail. I'm glad this was part of my assignment, and I feel a lot more confident about AP statistics! The school year will be quite different, of course, but videos like this are what will help me get through :)

[@texiediamond4693]

Love his teaching method.... Finally, I understand standard deviation right away with his method. Thank you so much :)

[@laurenback2192]

This helped lots with my research skills module as part of my psychology degree. Thanks for taking the time!

[@lukecrops1531]

3rd time I am watching this video for an exam, thank you for the last time, my last GCSE exam is in 3 hours!!!! WISH ME GOOD LUCKKKK!!!!!!!!

[@pwghost]

and did you pass ?

[@lukecrops1531]

I passed, I did ;) I am in college now

[@pwghost]

martin208398 COCMaster nice good luck with everything !! just curious, what are you studying ?

[@lukecrops1531]

Maths and Stats, Business Media (film studies) and Info technology :) I am boss in all my subjects but in maths I am slacking its really difficult.

[@cheyspodcast]

THIS WAS UNREAL. THIS VIDEO is the only video / way of teaching that has me finally understanding SD. Thank you so much! I'll be binging all of your videos now! haha

[@fabianloera1402]

Literally applying it in bio and it helped

[@arunulianchery135]

You are a gem!! Loved it. Will remember for long and you exactly helped me clear the confusion with the formula and how it really came into existence!!!!!

[@someswararaok7787]

This is very good to understand how to calculate standard deviation

[@quintonveach1922]

You should be a teacher. You make stuff that I would usualy find boring more enjoyable by your overall attitude and jokes. My teacher had even showed us your videos in class sometimes because he likes them so much.

[@whathaswings]

hes my teacher irl srs

[@ramakrishna2021]

The way you teach is wonderful. It easily reaches to all the age group. You 100% grabbed viewers attention through out the video.

[@afawkimartyr]

From all the videos I watched with lots of animations and high skills presentation, your video is the only one that gets my full respect ....I just want to say to you ....Thank you very much

[@RexGalilae]

This video saved my life back in high school :') thanks a lot sir!

[@Flopsaurus]

You are an awesome teacher.

[@jessicahall6549]

God bless you, you perfect person. I'm in statistics at my University and finals are next week and I've been struggling with standard deviations, because my professor didn't explain it well, and all semester they kept popping up. Now I get it completely! Thank you so so so much, you have saved my GPA and thus, my life.

[@ravells]

That was an absolutely brilliant explanation. Thank you so much!!! I've always wondered WHY standard deviations required you to square the figures in the dataset, now I know. Thanks again!

[@jaspreetsarveshk]

Thank you for this wonderful video! Enjoyed it. :D

[@sachinkainth9508]

Dude. You rule.

[@katherinemangum154]

I am an MBA graduate student and have never had a professor explain standard deviation as well as this video. THANK YOU for making a complicated problem seem easy.

[@michaelpsycho53]

I have a teaching demonstration on Standard Deviation coming up and this has helped a great deal on how to make it understandable. I love your charisma. Thanks so much.

[@deebadubbie]

What a great teacher!

[@yasirchoudhary824]

Now I Hope got the idea of Standard Deviation for lifetime . Great Video :)

[@n2cheese]

Love your dad charisma and simplified teaching! Thanks!

[@alixgomes2266]

This was so helpful, it helped me feel capable, and I really learned how to find the standard deviation lol! I absolutely love your charisma!

[@MrMikomi]

Wow, you are good! I wish all teachers were as good as you! Thanks very much for this.

[@eustacefan]

and as good-looking lol

[@Oxygencat]

wow you're a great teacher and so cute!

[@MSG9876]

This guy is awesome. Not in a million years did I think I would get this stuff. He makes it obtainable. Thank you very, very, much!!! You rock!!!

[@curtcleancut]

This guy's videos are freaking carrying me through one of my master's courses. Keep up the great work brother! I was watching one of your other videos and saw the Boston Sox cap. If you're a fellow local, I owe you a Dunkin Donuts coffee.

[@raymmmmm]

One small problem which might confuse a lot of people here. Taking the root of the average squared distance from the mean does NOT give you the average distance from the mean. In fact, standard deviation is technically NOT the average distance from the mean (thats where his "sort of" disclaimer kicks in). You can take a look at his example, average distance of {1,2,3,4,5} from the mean is 1.2 but root of the average of squared distance from the mean, root 2, is not 1.2. This still doesn't answer the question, where does the formula come from? Why take the root of the mean of the distance square instead of mean of the positive root of the distance square (which is actually the average distance of the mean).?

[@MrNystrom]

yes. true. for pedagogical reasons that was left out. Notice that I say "sort of". thanks for watching.

[@MA-vy8kl]

+Raymond Foo Yes thats true. Did you figured out why?

[@jeffgalef121]

+Raymond Foo Thank you for pointing this out. I just realized this last night, and was watching this video hoping to get an answer to the question of why do it this way. Taking the average deviation from the mean seems to make a lot more sense.

[@jeffgalef121]

+MrNystrom Could you please explain why it is done this way, and why this is more useful than calculating the more intuitive average deviation from the mean? Thanks.

[@omarabid]

I'm sorry this doesn't make sense. Your whole explanation is incorrect in that case.

[@brianmerritt5410]

That's it. I'm subscribing to this guy.

[@kitian1830]

Awesome explanation - after trying to understand this for years, this explanation was what I needed haha the concept will stay in my head for ever lol great job!

[@darjodey]

Mr. Nystrom, you are still helping people in 2021. I'm in grad school and need to know this for assessment purposes. You saved me from despair. Grateful.

[@angrycoder5520]

makes me feel like I am a stupid kid seating in a class again.

[@MrNystrom]

Sorry about that. It was not my intention. Best of luck on your stats quest

[@kathrinehansen9573]

+Lee F Why did you see the video then? It helped a lot!

[@I-believe-in-humanity]

This guy is the Real Teacher !!

[@shekharkaul]

Man I couldn't stop myself from writing a comment before even I could finish up with the video.. You are awesome, Thanxx mate

[@strikerdubzee9300]

Honestly my prof could not get this into my head any quicker. I like the style you have with breaking down a formula with definition and explanation of the reason behind it!

[@dynastyman36]

wow helped a lot. my chinese stats teacher has a strong accent so i have no idea what he's teaching.

[@HighCrafting]

Great enthusiasm and teaching style. But why was I taught to divide by (n-1) ? I'm so confused. Stats test on Monday :(

[@MrNystrom]

think about another measure of spread.. like the range (high-low). think... what would be higher.. the range of a sample or the range of the population you took it from??? I hope you can see that the population will most likely be higher because a small sample most likely won't have the extreme highs or lows.... we take samples because we are curious about the population.. so if you took a sample's range, you'd know it was probably smaller than the population's.. so you'd guess the population's range was a bit bigger. so you might add a little to the value when you guess the population's range. A similar thing happens with standard deviations.. when we take a sample SD... it tends to be a bit lower than the population's SD... but instead of guessing a bit more... we insert a fudge factor (n-1) in the denominator which adds a bit more automatically.. as the sample gets larger.. the n-1 has less of an impact, as it should, as you'd be picking up more extreme values as n grew. so if you have the population, calculate the SD with just n, because you have all the stuff. if you are using a sample to guess the population's SD, divide by n-1. does that make sense?

[@HighCrafting]

That makes sense when you say it like that, but my prof didn't explain it quite like that... Sometimes I swear he's speaking Greek. Lol! Thanks for the explanation.. Wish me luck!

[@joblesstess]

Erin Brooke McDonald Hi Erin, dividing by (n-1) is for sample standard deviation and dividing by (n) is for population standard deviation. I know this is late but oh well :)

[@HighCrafting]

Now that makes much more sense to me! Thank you for clarifying

[@sb805ca]

Erin Brooke McDonald

[@sabrinagruner8682]

Guy, you're very good on it!! Congrats!! Keep going, is your passion, and you deserve an oscar for this performance! Thanks a lot, pretty helpful!

[@johnathanparker2182]

Holy shit! You start with the most intuitive measures and build up to the "accepted" measures. I love you. I always wondered why there so much hate against absolute value when it's much more intuitive

[@Anooshehk]

Hi. I love your teaching method and thank you for sharing :) I have a question. Can you explain the difference between standard deviation and sample standard deviation. In the second one N become N-1 and I cannot figure out why. :) thank you again. loved your class.

[@olumideayegoro3857]

when you are given a problem set and you are to calculate the SD with a "sample" size, you are assuming the population size, so you must include (n-1) as the population number. If you are given the exact number of the population size, there is no estimation here, that is when you utilize just (N). I hope i shed some lil light on this

[@Strider_JM]

I'm in love with you right now, thank you!

[@daya512523]

I just love the energy you bring to the videos, helps with the learning process. you are so detailed, as I am a visual learner, a nurse and not in love with statistics, lol. Yet an area related to nursing is collecting data and evidence based practice. Thank You!!!! :)

[@dawnaweaver-hohall3860]

I love it! You make my everyday math face in my statistics class! You really help me understand standard deviation better than anyone else has. Thanks.You can teach an old dog new tricks! LOL!

[@NordikCreative]

You rock

[@nofinishhline]

ur a wizard. please by my teacher. thank you

[@MrBamshy]

Cannot believe standard deviation could be explained as simple and conceptually meaningful as this!!! Awesome job!!!

[@kelvinadimaswijaya9523]

Best explanation, best teaching, most passionate people i've seen in my entire life, thankyou

[@quetzalamaru]

super fun.

[@luisadituri6268]

You're like the Bill Nye of Stats. Thank you so much for this!

[@financeinsightswithtinashe]

Legendary lecturing skills !!!!!!!!!You are everything a lecturer/teacher can ever aspire to be !!! You Sir are a living legend

[@ambercohen1777]

3 minutes and 29 seconds in and you have blown my mind. Thank You. I now have a concept to hold on too.

[@JamieKingCS]

Eh, waaaaaaait a minute. So the "mean absolute deviation" is the actual average distance to the mean, which in the sample set is 1.2, but the regular standard deviation is sqrt(2), which is 1.41 But you call both values the "average distance to the mean." But 1.2 is not equal to 1.41, so which one is the average distance to the mean? 1.2 seems like the correct answer, so what does 1.41 buy us?

[@andriesliebenberg2368]

+Jamie King Thank you! I was looking for this comment as I have the same question. Did you ever figure it out?

[@josephnystrom7154]

+Andries Liebenberg The first one is the "true average distance to the mean" the standard deviation is "about the average distance to the mean"... We say "the average distance to the mean" because it is about the typical distance to the mean. It gives us something to relate to, (in this case, the concept of average and distance). The standard deviation is a tricky measurement that also accounts for variability within a set. I do not talk about this in introductory lessons as students will miss the point. The two sets 3, 3, 7, 7 and 2, 4, 6, 8 have the same mean, 5, and the same average distance to the mean, 2... Looking at these sets, which do you think has the most variability? I hope you think the second. The standard deviation takes this "variability within" into consideration and it shows up in the calculation because of the squared distances... So the standard deviation of the second set is larger than the first set. Even though they have the same average distance to the mean, the second is more variable....

[@josephnystrom7154]

+Joseph Nystrom t's like when you teach Pi... you don't say its "3.14159..... etc.." The correct way to teach Pi is to say "it's about 3" and use 3 for some calculations of area and circumference.. The fact that Pi is irrational is pretty cool, so using Pi as an introduction to irrational numbers is a good teaching approach, however, using the fact that Pi is irrational to introduce it is a HORRIBLE way to teach Pi. Students get lost in the mystery of irrational numbers and don't ever get to see that Pi is "about 3" ... Pi is simply how many diameters fit around a circle, and how many radii fit around a half circle (hence... radians...).

[@krishanveer8199]

@@josephnystrom7154sir, u just made my day. Keep sharing the knowledge.

[@niwashikun]

@@josephnystrom7154 Great video but IMO you should have included this info in the video. It's brief, simple and clearly clarifies what otherwise is a confusing takeaway from the video.

[@willjones1657]

Look at mah Stan-dard Deviation right-a there....

[@Fishtail3]

+William Jones Nicely done mah, I read it in their voice mah

[@jessicatusiime5899]

Literally the best mathematical video on KZbin, You just derived a formula, goodness, I cant believe how obvious you made this appear

[@margaretjudithvaynman]

Thanks that was so funny - helped me understand nearly impossible concept (for me) and most importantly, your video made me remember, through your use of humor and theater. Wish for you to produce more videos such as this one, covering topics that for some of us take forever to understand in statistics.

[@noelsamkomwa9165]

Can you please demonstrate where (n - 1) comes in sample standard deviation.

[@MrNystrom]

Noel Samkomwa A quick explanation... usually, we take a sample to find out about a population... We may take an average height of 30 random kids at a school to estimate the average height of all of the kids at a school. That would be using the sample mean to make a guess at the population mean.. If we used those same 30 kids' heights to estimate the true population standard deviation, we'd find that our sample standard deviation tends to underestimate the actual population. This underestimate happens over and over... SO... to make a better estimate, we want to make our sample standard deviation a little bigger so it estimates the population standard deviation better... we do that by making the denominator a little smaller, and alas... a slightly different formula..

[@Blasi1980]

MrNystrom mate you are epic

[@WorldBarbie]

ur amazing. thats the M=

[@sukannyajamadar]

Clear and consice explanation with comedy... couldn't get any better. Thank you!

[@osahonosa9186]

I'm taking classes online and that's already hard enough as it is. All I have to explain what to do on the test, homework, quizzes and everything in between is a video module, the book, my dad, and... well that's pretty much it. The rest is on my own. I'm so glad I clicked on this video because I've already learned so much in this one video than I have in the 4 chapters we've done as a class. BTW I LOVE your animated personality! keep it up and please don't stop making videos.