Calculating the Mean, Variance and Standard Deviation, Clearly Explained!!!

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One of the most basic things we do all the time in Data Analysis (i.e. Statistics, Machine Learning or any other sort of number crunching type thing) is calculate the mean, variance and standard deviation. This StatQuest walks you through these tasks and help you avoid a very common pitfall that is all too easy to fall into.
NOTE: This StatQuest assumes are already familiar with...
...Histograms: • StatQuest: Histograms,...
...Statistical Distributions: • The Main Ideas behind ...
...the Normal Distribution: • The Normal Distributio...
...and Population Parameters: • Population and Estimat...
NOTE: For more details on why dividing by 'n' underestimates the population variance and why we square each term, check out the follow up StatQuest: • Why Dividing By N Unde...
For a complete index of all the StatQuest videos, check out:
statquest.org/...
If you'd like to support StatQuest, please consider...
Buying The StatQuest Illustrated Guide to Machine Learning!!!
PDF - statquest.gumr...
Paperback - www.amazon.com...
Kindle eBook - www.amazon.com...
Patreon: / statquest
...or...
RU-vid Membership: / @statquest
...a cool StatQuest t-shirt or sweatshirt:
shop.spreadshi...
...buying one or two of my songs (or go large and get a whole album!)
joshuastarmer....
...or just donating to StatQuest!
www.paypal.me/...
Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter:
/ joshuastarmer
#statquest #statistics

Опубликовано:

30 сен 2024

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Комментарии : 560

@statquest 2 года назад

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

@adityaparab7802 Год назад

can you please make notes on fundamental of statistics

@statquest Год назад

@@adityaparab7802 A lot of these topics are already covered in my book.

@davidbrown2806 2 года назад

I have a Masters Degree in Economics, and with all the statistics lectures I have attended, I have never seen such a sensible and clear explanation of the topic.

@statquest 2 года назад

Thanks!

@Scrungge 2 года назад

Gives me confidence that I'm not the only one needing a refresher in the last year of my bachelor.

@hightttech 5 месяцев назад

@@Scrungge : 95% confidence?? 😃

@InfinitiCyberSolutions 5 лет назад

If only the math teachers I've had in the past taught the way you do, life would've been so much better. Just saying...

@statquest 5 лет назад

@fairuzam1420 4 года назад

@@statquest i like the way you say "BAM...!!!", And any other "sanguinis" stuffs. More jokes, more relax. Learning is fun gang...

@antoniojperezcastro5013 3 года назад

Agree. we need a calculus quest just like this one

@jlcgu11 2 года назад

Actually I give some credit to all past teachers. We understand better now because we've learnt a bit along the way, making things easier.

@mathivananperiasamy Год назад

If you would have been curious enough to learn, like you do now searching RU-vid, in your school or college days, your math teachers would have been like Josh to you. Just saying

@TheSunshinew 5 лет назад

I came here for Josh's music

@statquest 5 лет назад

You have very good taste in silly songs! :)

@devianttt94 2 года назад

Discovering this channel felt like I struck gold. Thanks for the awesome content!

@statquest 2 года назад

Thank you!

@vimalanatarajan9227 5 лет назад

Happy to have found your channel.. Thank you so much for all the hardwork you put in to help people...

@statquest 5 лет назад

Thank you! :)

@neerajanaghosh1007 4 года назад

It's really sweet how you guys make songs for really boring/difficult/important topics and make it so fun! 😁 Thanks a lot!!

@statquest 4 года назад

Thanks! :)

@ExceptionalPOV 4 года назад

This is the very first time I am commenting on my you tube career. We are very much honored to have you here. Thank you for your contribution to make this world a little more better place.

@statquest 4 года назад

Thank you very much!

@sloshy1840 11 месяцев назад

This has to be the most ADHD friendly math content I've ever come across!!! This is so brilliant and fun!

@statquest 11 месяцев назад

Thanks!

@darkreaper4990 3 месяца назад

Yeah, I have adhd too and was thinking the same 😂 it also helps that these videos explain the topics in a way that feels intuitive.

@anupkodlekere3633 4 года назад

This guy is just great. As soon as I wonder about something, he comes up with a Note and says the exact same thing holy shit

@statquest 4 года назад

Awesome! :)

@aparnajoshi2433 3 года назад

This is just amazing. I am going through a data science course and I have been coming back to this channel to strengthen my understanding of several basic concepts. Thank you so much for making these videos. Also, you sing well :P

@statquest 3 года назад

Wow! Thank you very much! :)

@shrutimishra5596 3 года назад

Which course..actually m also thinking of taking one it would be a great help if u ans my query

@adrianzhang9508 3 года назад

How come I only stumbled into this amazing channel just now???? Had my math teacher explained these terms/theories in such an easy and interesting way, I’d be working on building a rocket!

@statquest 3 года назад

Bam! :)

@Toirtapable 3 года назад

greetings form germany. U helped me a lot :)

@statquest 3 года назад

Glad to hear that!

@zeuspolancosalgado3385 2 года назад

Your RU-vid channel carried me through Probability & Statistics and Machine Learning

@statquest 2 года назад

bam!

@AizenMD 4 года назад

I love that he uses BAM a lot, it feels like a dad trying to be cool even though he is without trying and just don't realize that (hope that made sense XD)

@statquest 4 года назад

BAM! :)

@rajatrana2020 3 года назад

Hey Josh! I recently found your channel (while surfing for Covariance) and found these awesome videos you make! BIG HEARTFUL Thankyou!!! I have this one doubt. We square the differences to make sure there isn't any negative term and in the end do a square root to finally get the standard deviation. As it turns out, in the middle of this we have termed the squared result as Variance. I do not understand why we needed Variance at all? SD was what we were looking for and SD helps us understand how spread out the curve will be. Then Why Variance is needed at all? (Otherwise we could also raise the differences to the power of 4 and name the result something fancy like Ultra-Variance, and then fourth root of Ultra-Variance would be our SD)

@statquest 3 года назад

Standard Deviations are easier to interpret, but some times we only need to do relative comparisons. For example, I might just want to know if one thing has less variance than another. For relative comparisons, we can save ourselves the extra work of calculating the standard deviation.

@suhass6628 4 года назад

2:41 "It is the population mean".....savage!!!!!

@statquest 4 года назад

@juan.jose.111 4 года назад

I'm spanish spoken but somehow I truly note that great sense of humor you have.... my first option to learn statistics topics is this channel. greetings

@Terniedintorni 4 года назад

You are the best statistic teacher. Ever!!!! thank you

@statquest 4 года назад

Thanks! :)

@_Chafia 5 лет назад

Merci infiniment Dr Starmer... vous êtes le meilleur à expliquer des stats... et les notions de base sont très importantes.. je vous félicite pour le choix diversifié des thématiques 👍 Best regards Sir :)

@statquest 5 лет назад

Merci!!! :)

@CopyKitties Год назад

Thank you so much for this! I am in AP Stats, and I was confused on the difference between standard deviation and mean. Not only did it explain that, but it also cleared up my confusion on variance! Also, it was entertaining! Thank you so much! If I ever have trouble with math again, you’re the first channel I’ll turn to!

@statquest Год назад

I'm glad my video was helpful! :)

@sivagurunathanparanitharan4714 4 года назад

🙏 May the almighty God bless you with health and wealth and a Joyful Long Long Long Life, Thank you indeed 🙌

@statquest 4 года назад

Wow! Thank you very much! :)

@shamsulazhar 2 года назад

I came for the sweet-sweet music.... I stayed for the educumacaysion

@statquest 2 года назад

bam!

@octour 5 лет назад

Thanks. As always - very simple, and useful! But still I can imagine, what work you've done with animation, and presenting that material.

@statquest 5 лет назад

I dream of one day animating my StatQuests. Some concepts would really benefit from it.

@chrisvaccaro229 4 года назад

@@statquest I think you'd be surprised at how easy software like Adobe Animate are. Also, 3Brown1Blue just uses python to make his videos.

@suman-by7gt 2 года назад

Wow wish I had had the good fortune of your teaching during my academics. However thank you for the wonderful n easy explanation... And thoroughly enjoyable

@statquest 2 года назад

Wow, thank you!

@dsagman Год назад

I am unreasonably excited for the “beep boop” of the algebra.

@statquest Год назад

That's awesome! BAM! :)

@kenadams-zu4ds Год назад

What a good deed I have done, God rewarded me by finding this channel. I'm so glad to have you.

@statquest Год назад

Wonderful!

@MuhammadHassan-qj7do Месяц назад

Outstanding and exceptional job... you are doing. Trillions of thanks and appreciation. Extremely pleased to have your channel.

@statquest Месяц назад

Thank you!

@edwardgrigoryan3982 2 года назад

Thought I knew the basics well, but I'm truly mastering them now as I go through your channel. Thank you!

@statquest 2 года назад

I'm glad my videos are helpful! :)

@kandycane4751 3 года назад

Man, I just love the way you did explain everything cuz boi I truly was struggling to understand it. YOU ARE DA BEST

@statquest 3 года назад

Glad it helped!

@bluebottle548 Год назад

Sir I have a question I just wanna know whether this n-1 applies for compensation of population variance in only population data generating NORMAL DISTRIBUTION or Any DISTRIBUTION in general 🤔

@statquest Год назад

See: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-sHRBg6BhKjI.html

@kajalraut4185 2 года назад

You my dear are life saviour❤. Finally understanding the Statistics after spending 24 years on this earth. Thanks a lot and Keep up the good work 🤓.

@statquest 2 года назад

Thanks!

@ashleysullivan7965 Год назад

Finally, an answer to the vague nagging concern I'd had when VAR.P and VAR.S both show up in the context clues working in Excel for years... Hah, thanks!

@statquest Год назад

Glad it helped!

@fatematania2193 6 месяцев назад

Execellent lectures. Your lectures are presenting statisitics as almost new to me. Could please add some more explanation on how (n-1) compensate in estimated population variance? I am grateful to you for your contribution to my learning.

@statquest 6 месяцев назад

See this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-sHRBg6BhKjI.html

@emmaxu2001 3 года назад

As someone who tries to figure out the concepts but often put off by the math formulas, your channel made it so simple and easy to understand!

@statquest 3 года назад

Thanks!

@goktugmk 5 лет назад

You are great. Complex issues can be easily undertstandible by your videos. Thanks for these all videos.

@statquest 5 лет назад

Thank you! :)

@shuflee2754 5 лет назад

Same with Python numpy. The sdv function returns the population standard deviation by default. You have to ascertain by assigning ddof=1.

@statquest 5 лет назад

I didn't know that. Thanks for posting. :)

@rodrigogs9793 Год назад

This is probably the very best video about variance, standard deviation I've seen. It's great explanation

@statquest Год назад

Thank you!

@bakhodirjonkakhkharov344 3 года назад

It seems that schools should stop organising live lectures and show some cool educational videos from RU-vid instead! Nowadays, we are learning more on RU-vid than we do in schools

@statquest 3 года назад

bam!

@tonyle876 4 года назад

thank you Mr. Starmer very much, wish my ML lecturer taught me like this .... and not just toss fancy formulas and words (variance, deviation, ....) onto my face everytime ..... it`s not so hard finally^ just needs to be explained well, in understandable way .....

@statquest 4 года назад

Hooray! I'm glad my videos are helpful! :)

@LukePuplett 3 года назад

I was thinking, "I often see things squared like this, and it often doesn't seem like it would make a difference to the outcome, I wonder why they do it?" No sooner had I thought it, you explained why so clearly :-D Bravo, sir.

@statquest 3 года назад

bam! :)

@SuperGozookkk 4 года назад

Wow,you are the best statistic and machine learning teacher.Thank you

@statquest 4 года назад

Thanks! :)

@AndrewSitholeB 4 года назад

wow this was so good....i really enjoyed the time cause it was very clear

@statquest 4 года назад

Awesome, thank you!

@ec7283 Год назад

You should also start a cover carrier of Bill Callahan, unless you are him under false identity...

@statquest Год назад

Ha! :)

@castimann 2 года назад

I still didn't see the video but I already gave you thumbs up for that super cool introduction.

@statquest 2 года назад

@fairuzam1420 4 года назад

please make some video of how to measure data in SPSS or any statistical computer application. I LOVE YOUR VIDEO

@vahidnajafzadeh4137 3 года назад

all my life I have always been avoiding stats because I thought I was stupid and it was hard for me. now I realize my math and stat teachers were all stupid with zero interest in what they were teaching. thus wasting our precious childhood time and life. thanks for all these great tutorials 💚.

@statquest 3 года назад

Better late than never! :)

@datalearn-zv4dt Год назад

whenever I rewatch this video, I always laugh out loud at the part: be doo booo too be doo be doo be doo :))

@statquest Год назад

bam! :)

@vedantshirodkar Год назад

Thank you for all your efforts. Each video is just right enough to provide you entire knowledge one needs.

@statquest Год назад

Thanks!

@joxa6119 3 года назад

If only if I found you before I need to repeat my Statistics course in my first year of study...

@statquest 3 года назад

@shivanshjayara6372 3 года назад

U R GOD in explaining things which are so much difficult

@statquest 3 года назад

Thanks!

@pratik2886 4 года назад

Excellent..Commendable...well done.. Just the kind of explanation I was looking for.

@statquest 4 года назад

Thanks! :)

@kumarvivek1866 5 лет назад

Thank you for explaining deviation in deep and I'm looking for such explaination cause in my college they told us to mug up whole formulas instead of making us understand where the formulas come from. Thank you From 🇮🇳

@statquest 5 лет назад

Hooray! I'm glad that the video was helpful.

@matrixbegins 2 года назад

I love your BAM!!!! and Terminology alerts :)

@statquest 2 года назад

Thank you!

@santoshgujar5237 2 года назад

Thank you, Sir, you know Gracie Terzian, The Ukelele Player

@statquest 2 года назад

Bam! You're binge watching StatQuest! :)

@anishchhabra5313 2 года назад

Hey guys please check out Josh's : "Why Dividing By N Underestimates the Variance" video, it is awesome.

@statquest 2 года назад

BAM! :)

@anishchhabra5313 2 года назад

@@statquest 😂😂 Double Bam!!

@rortanachea 3 года назад

I am working on colony forming unit of coagulase positive staphylococci. I grt cfu/g of meat sample and transform to logcfu/g. To analyze this data , i use mean and standard deviation. Abong 532 of our samlle, some Of them gave zero cfu. Results show sd even higher than mean. Is this correct?

@statquest 3 года назад

I have no idea. :(

@rortanachea 3 года назад

What can we do with zero?

@marjiehoss1498 4 года назад

I came here for the learning stayed back for the learning and the rad music

@statquest 4 года назад

BAM! :)

@ritshpatidar 9 месяцев назад

I wasted my precious time on Khan Academy, Wikipedia, and Stackexchange to understand just normal distribution fully.Thank you so much for explaining it in 2 videos.

@statquest 9 месяцев назад

Glad it helped!

@MrEstebanEscudero 4 года назад

Great video! It really helps watching the images and colors along with arrows and text to better understand. I typed "variance and standard deviation" in the youtube search box and StatQuest popped up. I know the quality of your videos and that's enough reason to watch yours among others. I didn't need to look any further. Priceless info. Great teacher.

@statquest 4 года назад

Thank you very much!!! I'm really happy you like the videos. :)

@charlesnorvow 3 года назад

Mr. Starmer, you are so brilliant! Thanks for your contribution! I just found your YT videos and they are fantastic. Please keep up with this great work!

@statquest 3 года назад

Thank you very much! :)

@ricardofranco-duarte346 4 года назад

Having a so small dataset (in this case 5) how do you know that it will follow a normal distribution?

@statquest 4 года назад

A lot of things are normally distributed because they are the sum of lots of little processes and the central limit theorem says that sums of things are normally distributed. See: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-YAlJCEDH2uY.html

@46ketantodkari35 3 года назад

videos are very helpful .thank you so much.

@statquest 3 года назад

Thanks!

@hughjazz4736 4 года назад

I thought you were gonna sing the whole vid notthatimdisappointed

@statquest 4 года назад

;)

@carltoncotter2614 2 года назад

Josh - just relearning this after some years. Quick question - would all the math be the same for a "population" of values that were both positive and negative? For example, daily change in temperatures above and below a mean? In that case, would negative values go off to the left for values below the mean and positive values go to the right for values above the mean? But otherwise the mean daily change would be the center of the curve (assuming normal distribution)? Variance average of the differences squared? And 1 SD the square root of the variance? Thank you and subscribed!

@statquest 2 года назад

Yes, you are correct. Bam! :)

@maxchan5956 2 года назад

Now I BAM on all my statements. Triple BAM

@statquest 2 года назад

BAM! :)

@Dominus_Ryder 4 года назад

Hello again Josh, Wonderful video, however, I was wondering if you can clarify what you would do in a situation where you were measuring mRNA transcripts from multiple Gene Xs? In such a case you would have multiple sample means, and multiple sample standard deviations. It feels like you should be able to aggregate all the different sample means and sample deviation calculations somehow to get an even more accurate estimation of the population mean and STD. In your video you describe how your estimated accuracy would increase if you increase the number of green dots used in your calculations. However, what do you do when don’t necessarily have more green dots to use, but have multiple sample estimations of the mean and STD? Thanks again for all of your help! 🙏

@statquest 4 года назад

That's a great question. Yes, it is possible combine measurements from multiple genes to get a better estimate of the mean. Are you familiar with edgeR and DESeq2? These programs compare gene expression, as measured by high-throughput sequencing reads per gene, between different experimental conditions. For example, we could use edgeR or DESeq2 to identify which genes are differentially expressed between a normal and a diseased liver. Anyway, there are typically very few replicates for each condition (often there are only 3 measurements per gene for "normal" and 3 measurements per gene for "diseased"). However, they have measurements for close to 20,000 genes. So, both methods have ways to "aggregate" the information across genes. For DESeq2, it groups genes with similar means together to get a better estimate of the true mean. I'd recommend reading the DESeq2 paper, since it is relatively easy to read and has a nice figure to illustrate what's going on.

@Dominus_Ryder 4 года назад

@@statquest I'll definitely look into that paper. However, I have more of an engineering background, so I was just using the mRNA transcripts example because that's what you used in your video. I actually wanted to know if there was some sort of general statistical method or test that could be employed, in a general case for all research fields. However, i'll take a look at the paper anyway since it's so highly recommended by you. Thanks for taking the time to get back to me.

@statquest 4 года назад

@@Dominus_Ryder Here's the link to the manuscript: genomebiology.biomedcentral.com/articles/10.1186/s13059-014-0550-8 In figure 1a, you see how the mean values (black dots = MLE = maximum likelihood estimate, which is the mean) are pushed towards a smoothed "prior mean" (the red line, which is the result of combining measurements from all of the genes).

@achannel9598 2 года назад

instead of plugging in the numbers and calculating with no explanations of the formula like how my teachers did, you gave explanations such as why we had to square x - μ. Thanks!

@statquest 2 года назад

bam!

@yingc1233 2 года назад

Amazing videos Josh, thank you!

@statquest 2 года назад

thanks!

@drewfrench8784 2 года назад

Thank goodness for you sir. The class I am taking is like " So. You now know how to calculate a mean. Please find the p-value for this sample population in hieroglyphics using Python."

@statquest 2 года назад

Bam! :)

@sivabonthada1076 3 года назад

My bad. I found this channel very late.

@statquest 3 года назад

@ibritics 3 года назад

Relatively small size -> 5 out of 240 bln ahah

@statquest 3 года назад

@lidiyapriyadarsinik2815 3 года назад

These videos make stuff so simple and easy, I relax and get un-depressed. It's like meditation. Thank you.

@statquest 3 года назад

Glad you like them!

@supriyamanna715 2 года назад

if I am not wrong, you're a faculty at Netaji Subhas Engineering College at Kolkata? and obtained your degree from AP?

@ahmedaraby1113 5 лет назад

thank you very much for these amazing videos.

@statquest 5 лет назад

Thanks! :)

@batoulmed6449 2 года назад

well explained and organized, thank you

@statquest 2 года назад

Thank you! :)

@THEMATT222 2 года назад

Do you know why the world is a cruel place? ....because the average person is mean

@statquest 2 года назад

Triple bam!!!

@THEMATT222 2 года назад

@@statquest Noice 👍 Doice 👍 Ice 👍

@siddheshb.kukade4685 2 года назад

Hey bro Idk who you are untill now but our teacher just did a 1 hr long lecture explaining your video frame by frame. Just wanted to let you know that your content is creating big impacts 🙏👍 keep it up💯🔥

@statquest 2 года назад

Bam! :)

@memeingthroughenglish7221 Год назад

Cool explanation of where the n-1 comes from! I never would have guessed that it is to compensate for using a sample, but that makes sense!

@statquest Год назад

Thank you! :)

@abhasmalguri2905 Год назад

Really very good videos. Easy to grasp. Thanks for this amazing content👍

@statquest Год назад

Thanks!

@unpatel1 2 года назад

Thank you for your clarification about n-1!

@statquest 2 года назад

Thank you!

@pedrodcthe1 Год назад

It's awesome when an explanation generates a question in my mind and the next step is the answer to that question. It happened in the end when I wondered which formula did the common softwares used for var and sd. Thank you for your videos! From Argentina

@statquest Год назад

Muchas gracias!!!

@pingyang6385 3 года назад

HI, josh, i watched all your stat videos, they are indeed veery good and very clear. I am wondering whether you have related notes or ppt for sharing. thank you!

@statquest 3 года назад

I have study guides for some of my videos here: statquest.org/studyguides/

@chanroobi7460 4 года назад

Taking Stats at University of Texas and I feel like I am standing before a tidal wave. I hope these videos help.

@statquest 4 года назад

Me too!

@rg1957 3 года назад

Thanks a lot for these wonderful lectures.. I am so happy that I can follow the lectures with ease as if watching a movie... With all good music and BAM!!

@statquest 3 года назад

Bam! :)