Standard deviation (simply explained)

The most common measures of dispersion for metric variables are the standard deviation and the variance in statistics. These two measures relate each expression of a variable to the mean and indicate how much the individual expressions scatter around the mean.
What is the standard deviation and how do I calculate it?
In statistics, the standard deviation gives you the spread of a variable around its mean. The standard deviation, is the average distance of all measured values of a variable from the mean of the distribution.
The measure of dispersion standard deviation thus indicates how much the individual values scatter around the mean value. If the individual values scatter strongly around the mean, the result is a large standard deviation of the variable.
Sorry, in the example of course a standard deviation of 11.50 comes out and not 12.06!!!!
► Calculate the standard deviation online
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0:00 Introduction
0:22 What is the standard deviation?
2:16 How do I calculate the standard deviation?
4:09 Why are there two formulas?
5:59 What is the difference with variance?
7:17 Calculate the standard deviation online.

[@datatab]

Sorry, in the example the standard deviation is of course 11.50 and not 12.06!!!! If you like, please find our e-Book here: datatab.net/statistics-book 😎

[@andym1672]

How did you get 11.50 please?

[@ajsanpedro]

@@andym1672 if you use /n-1, you will get 11.5, but if you use /n, you will get 12.6. Because it's a sample size, you use /n-1

[@zehraseraparici974]

@@ajsanpedro If we use 6, the result is 11.5. Thank you!

[@Kripalu_das]

The way you say "Standard Deviation" is so cute

[@orca_ball]

I was calculating again and again and getting the 11.5036 but you keep telling 12.06 that was really frustrating. but thank god I checked the comments

[@user-rd3jw7pv7i]

Thank you random german woman on the internet. You don't understand how much this help me to go through my finals 😭 God bless you :)

[@datatab]

Many thanks for your Feedback! Actually I am from Austria : ) Regards, Hannah

[@muhammadomarkhayyamkhan3593]

Very well explained

[@thatwhit1]

There was a time when Austria was within the standard deviation of Southern Germany!

[@rasheedrahman1635]

😅

[@Peter-df2ip]

😂

[@magiciansway]

Many thanks. I am 62 and this is the first time I have a clear understanding of standard deviation. I also feel happy hearing you happy demeanor. Thanks.

[@norencezyron.bedasua]

I don't understand why anyone would height this video. That was very clearly explained. Thanks!

[@WilliamAlanPhoto]

It's a bold social experiment to calculate the standard deviation of hate. I salute you.

[@datatab]

Yes a little embarrassing, but you never stop learning : )

[@alexpower9423]

Hate is a mean value

[@speedomars3869]

Never forget, the results of ANY calculation depends on the quality and quantity of the data. In regard to hate, it is impossible to measure, impossible to determine and impossible to calculate because hate cannot be quantized.

[@alexstickney156]

Hoe many languages do you speak?

[@phychemnerd]

​@@datatabThat Austrian accent is actually adorable 🥰. Great explanation of the concepts as well!

[@johnieday5186]

As a psychology student I'm a bit dense when it comes to numbers and I need to know them. This really helped me keep up the good work and thank you!

[@datatab]

Many thanks : ) Regards Hannah

[@neisovo8177]

same! I was just watching a talk about autism and whenever the speaker mentioned standard deviation I didn't know what he meant, this was so helpful

[@purplecrayon7281]

if you are majoring in any science or business field in an American university, you will be required to take a introductory Statistic course in your freshman year.

[@johnieday5186]

@@purplecrayon7281 I’m in the UK but yes we have to study it

[@AR-tx4ho]

Do you have any interest in research methodology and psychoanalysis?

[@lauramandea348]

I have a statistic test in a couple days and this video explained everything that i didn't understand in a month in just 7 minutes. thank you from Italy

[@Potencyfunction]

It is 10 grade subject in "Math for 10 class/year " Is under section "ungrrouped obsevations" chapter. There you start learning "Average function" and "Median function ", Boxplots, Outliers and next statistic is the "grouped observations" where you learn calculating the "hyppighed" ( the most meated observations on the set " and the "frequency" on the bar chart . ( y axis ) . There you already got a fundament for buliding the continous learning goal, if you are planing to make vertical learning and obtain a crazy certificate of math or datalogist.😈

[@robindhood9125]

I kept hearing “hate” every time she said height; thankfully there were visuals. Great video and explanation, now I’m off to get my hearing checked.

[@motivatedguy387]

It's her accent not your hearing. Felt same fffs

[@SprakanaKerum]

They measure hate 😂

[@nizar4876]

You have explained very clearly and slowly to make understand us! Thank you a lot! 👍

[@musicsang4882]

Ma'am I pray to God that you live long and achieve whatever is best in your life. You are such a knowledgeable person who help us a lot. Thanks a lot. A big salute to you.

[@vishnumoorthy8859]

Such a simple explanation. Love it when people who knows stuff explain things.

[@subhasisghosh66]

Absolutely no idea why this showed up in my feed, but I am glad it did. Thank you for the succinct explanation.

[@piotrrybka318]

Nice video, but what is missing are answers to the following questions: Why in standard deviation we use quadratic mean instead of absolute value and arithmetic mean. What is the advantage of using quadratic mean? And why quadratic and not cubic? Or fourth power? Tenth power would also look nice and could be easier to remember. You say that it would be always zero, but that is not possible if absolute value was used. In your example the arithmetic mean of all height deviations is 10.(6). Why in standard deviation for a sample we exclude 1 value? And why only 1, and not 2, or 3, or 1.5? This does not seem too inclusive and equalitarian. And why excluding and not including? Excluding will distort the result value making the standard deviation seem greater that it would be if used the population formula. But it seems very arbitrary that the compensation for using a sample instead of the whole population would only be 1 value and only excluded, not included. Why the variance is 1 step behind of standard deviation? It could be considered as standard deviation squared, but the result would be the same. You correctly explained that standard deviation has the advantage of preserving the order of magnitute or the units. But what does variance mean? Preserving units means we can compare standard deviations measured for different samples, provided that the units, or more accurately, the thing we measure are really comparable. E.g. I can compare standard deviations of heights measured i USA and in UK. But does the variance allow for comparing, say, height and pay deviations? That would be cool and useful, but I guess squaring would not allow for it? If all that was explained, then and only then the standard deviation (and variance) would be really simple. Right now it is still a formula with some elements of it seemingly randomly assembled that can be only mindlessly memorized but not understand. For me keeping things simple does not mean expressing it in a simple language with even the best visuals. That is only half the job. But you also need to justify that every piece of information is logical and can be deduced without having to memorize it mindlessly. Then if you forget the formula or its part, you would be able to reconstruct it in full.

[@murilofernandes3492]

I also tried ti understand these points without success...😒

[@kimbott4963]

Love how simple and straightforward this video is. I'd love if it included why we use the n-1 in a sample case. I realize that would add significantly to the length of the video but it's conceptually pretty cool and a useful thing for more people to think about.

[@halfsourlizard9319]

Would have at least been useful to have mentioned the name 'Bessel's Correction' in case anybody wanted to read further.

[@yogeshmahindrakar4496]

Short and sweet explanation. I'll never forget standard deviation, variance and its formula.

[@datatab]

Thanks!

[@haylie7931]

Thank you for your amazing videos! True help to the people who struggle with numbers, but need it in their professions. Greetings from Lithuania!

[@user-py1jl8ds8z]

Finally I'm able to actually understand this thing after years. Very well explained indeed! ❤

[@Manasika]

You have explained very clearly and slowly. Such a simple explanation. Keep up the good work! Cheers! Thank you a lot!

[@tarunaggarwal2511]

one of the best-detailed example, I have ever seen....i dint think I will ever forget this

[@datatab]

Many many thanks!!!!! Regards, Hannah

[@Ghinan_Navsih]

This was really informative and easy to understand. You earned a subscriber today! Thank you

[@datatab]

Awesome, thank you!

[@thomasstevenrothmbamd2384]

This is excellent. Thanks for your help in educating our world about such important things.

[@dibinjoseph296]

Wow! So concise and clear. Visuals helped too. Thanks!!😊 Keep up the good work! Cheers!

[@mayerlysanchez1843]

This video really helped me to understand the concept of standard deviation. Specially the example. Thank you so much!🤗

[@CuriousCyclist]

Thank you for taking the time to make this video. Much appreciated.

[@user-vk3sf2qp4d]

excellent presentation in a very simple and digestible way. thank you. thank you from my heart since you simplified it so much .

[@cliveradvan3414]

If only this was explained as you did, when i was at school.... Very well presented. Thank you

[@Dooshanche]

Such a simple explanation, thank you!

[@datatab]

You're welcome! Many thanks for your nice feedback! Regards, Hannah

[@75blackviking]

Hands down the best and most succinct explanation of std dev I've ever seen.

[@kennethhowell5291]

Thank you for the clarity as to standard deviation. You are the best!

[@datatab]

Happy to help!

[@SD-un3ii]

Thank you very much for this simple explanation. I request you to please make similar type of video on Z Score and it's significance and comparison with Standard Deviation. Hoping to see this shortly.

[@88spaces]

It really helps me to grasp topics when they are simply explained which you did. Thank you.

[@datatab]

Glad it was helpful!

[@ianchikopela1003]

Ma'am, you are awesome. The simplicity exeh! Usually people come to KZbin when in dire need of simple, straightforward, i-am-dumb step-by-step explanations. And you, you just did that. You just provided that. YOU AWESOME!

[@datatab]

Thank you so much 🙂

[@LalitKumar-nj7xc]

Clarity and pace of your voice is making it very easy to understand.

[@datatab]

Thanks : )

[@NyanLinHtet-fi7ud]

As an online college student, I have some problems with this. This helps me to understand and thank you so much.

[@datatab]

Thanks!

[@karlostj4683]

"Here's an example. Let's say you measure the hate of a small group of people."

[@ajitmishra7666]

A beautiful lady explaining conceptual topic beautifully... thankyou ❤....now I understood the concept

[@deeladils8428]

Thankyou so much, everything i wondered is covered here. I always ask why we use quadratic on variance and never thought if doesnt it will always return 0! I'm very new in statistic and videos with amazing details like this (and beginner friendly) is so rare.

[@datatab]

Happy to help : ) Regards Hannah

[@auberonarlo3703]

The explanation is on point and easy to understand. Thank you DATAtab :)

[@datatab]

Many thanks for watching and for the feedback! Regards, Hannah and Mathias

[@mm0dk0ur]

I really want to thank you so much for your great videos and how you explain all concepts in a very clear, simple way. Thanks, please continue posting videos my dear German lady. Wish you all the best 🙏🙏

[@malhargawade5779]

Very well explained.....my teacher skipped the logic part and directly gave the formula to follow and i couldn't get it....this video helped me

[@vovk_oleg]

Please do not stop posting your videos. Very helpful. Other creators stopped.

[@mariateran9189]

I love you!!!! i procrastinated on doing some homework but after 3:20 minutes into your video, it all clicked! loved how well you explained this and your accent kept me engaged!

[@datatab]

Many thanks for your nice Feedback!!! Regards Hannah

[@gareth0000]

Thank you so much. I needed some rehresher on standard devaitation and have been watching more than 10 videos of standard deviation. This one’s the best, you have explained the practical application as well. It becomes so simple when you understand WHY and HOW we use it. I just flipped for a bit when you first said that that we or going to measure the standard deviation of “hate” of the people. 😂😂😂 then you started showing the height of the samples. Peace! English is also not my first language so I find it funny because I can totally relate.

[@datatab]

Oh thanks! I did not notice that : ) In the current situation hate would even fit : ( Regards Hannah

[@mohammadyaqoob8653]

very well explained, great job DATAtab

[@datatab]

Many thanks!

[@godawgs4536]

This helped me a lot. My teacher is away getting married, and we got a paper on this. We've never done it before, so I was confused.

[@datatab]

Happy to help! Thanks for you nice feedback! Regards Hannah

[@user-vs8pb4lg5m]

thank you from my heart since you simplified it so much 👍

[@jisancy5423]

3 weeks of my college in 7 minute Thank you very much

[@datatab]

Most welcome 😊 And thanks for the nice feedback : )

[@ademashyngyssova3582]

Thank you very much!!!! This channel really helps me to prepare for assignments!! Your explanation is really easy to understand. From 7 minutes video I learnt more than 6 weeks of my module! 😭❤️

[@user-gd5io7zi9u]

Very well explained! Great job!. Thank you for taking the time to make this video. Much appreciated..

[@davepickering997]

You explained in one video that took me years to understand to get a MSC.

[@SonaliSingh-mm6kz]

Simple and clear explanation.... Thank you❤

[@datatab]

Glad it was helpful! Thanks for your nice feedback! Regards Hannah

[@gulomjonsulaymonov5958]

before watching this video, I watched other 3 and I understood nothing, now I see this one and I understand everything just in 7 minutes, thank you huge

[@datatab]

Many thanks!

[@thehumbleone1936]

Amazing way of teaching! I love your explanations.

[@datatab]

Many thanks : ) Regards Hannah

[@user-me2np8ge3n]

excellent presentation in a very simple and digestible way. thank you

[@datatab]

Glad it was helpful!

[@maniaphobia4719]

I remember in 80’s my Maths teacher who was a terror ; We simply learnt out of fear ; This video makes learning damn easy

[@sidoniaachan1325]

Thank you for this , was stuck. Sending love from South Sudan,Africa !!

[@datatab]

You are so welcome!

[@VedantAdvait]

You said "hates" but I got that. You are correct if weight is pronounced as way-ate, then height should also be pronounced as hey-ate. This language issue has baffled us (Indians) too.

[@antoniolopezgomez1188]

Finally I got to understand what the std deviation is! Great video

[@lxathu]

Thank you, but... something always bothered me with SD but I never dared/could ask. I see that we square the differences so that they don't cancel out each other but actually we wouldn't have to: summing the absolute values of the differences would work just as well. From other sources, I understood that squaring distorts, enlarges big differences from the average which is good but there's no explanation why. Why can't we examine the differences from the mean just the way they naturally are, by averaging their absolute values instead of squaring them and square rooting after summing? If I got some explanation for this, probably 30 yrs of mist in stats would disappear.

[@piotrkrajewski9059]

This is exactly what occurred to me after watching, please elaborate on that dear author.

[@marcusaureliusf]

Me too. I know the "what" but they rarely explain the "why", i.e. why do we square things, why do we divide by n-1 (how does it help anything?), why we need both variance and standard deviation if both are so similar, etc. why?

[@Flexpicker]

One of the problems with taking the "absolute deviation", which is what you have described and is a possible means of looking at the deviation, is that it is not differentiable at zero. When you take the standard deviation, it results in a smooth curve. Another factor is that the standard deviation more closely represents the Gaussian distribution, which is one of the more common types of distributions due to the Central Limit Theorem. My hypothesis is that the absolute deviation would be better for a uniform distribution, but someone more knowledgeable should correct me if I am wrong.

[@doctor_gee]

The standard deviation method gives a useful insight into how much the data varies, more so than just summing the differences and dividing by the number of samples gives. Take this really simple example. 5 people with heights of 160 154 155 156 150cm The mean is 155cm If we simply take the average of the absolute difference from the mean we get 2.4cm This sounds fine at first, but look at the total range of the values, it's 10cm, so is 2.4cm a useful metric of the data? The standard deviation of the same data set is ~7.2cm, much more realistically representing the core set of data in the "range", as hinted at by @Flexpicker below. I'm not sold on how useful the "variance" is though! The squaring and then square rooting helps to make it into an easy formula and removes the negative values created by choosing which order to subtract the values in said formula. The same method is used to measure AC Voltage, the mean would always be zero, so we take the RMS (root of the mean of the squares) which gives a useful metric of any data set that includes both positive and negative values. Hope that helps someone.

[@seaglass8305]

Thank you for making it so clear!

[@datatab]

Glad it was helpful!

[@desisto007]

What a beautiful definition!!! So simple!

[@florin-titusniculescu5871]

" let's say you measure the hate of a small group of people " 🤣

[@delliscool4924]

Thank you so so much, Please continue to post such interesting math lessons.

[@kowtharhassan882]

Thank you. What if you take 2 samples, do u then divide by n_ 2?

[@knowledgeseeker97]

Hi miss, I am glad that I found you . Thank you so much for teaching us .This really helped us

[@godwinnwaokike]

This is so appreciated! Very well explained! Math can be fun if well explained.

[@monireachtang712]

The explanation is very clear and easy to understand. Thank you for sharing 😉

[@datatab]

Many thanks!

[@ikm64]

Something to thank you for - an education... and that's exactly what I'll do...Thank you!

[@datatab]

Thank you so much : ) Regards Hannah

[@pmpeepx]

Thank you for smooth teaching

[@datatab]

You are welcome! : )

[@shinjokagama7521]

This is the best explanation. Helped me a lot. Thank you.

[@rajnish570]

Very well explained, finally understood why Standard Deviation is important. Thank you so much 🙏👌

[@datatab]

Happy to help

[@joshuamcnab9605]

Thank you so much! I am a simpleton so this really helped me

[@datatab]

Thanks for your feedback!!! Regards Hannah

[@AdityaKumar-ij5ok]

Your smile makes this look so easy. Thanks a lot!

[@datatab]

My pleasure 😊

[@ronaldmarcks1842]

Short and sweet, thank you!

[@kuyakambo2327]

New subscriber here from the Philippines. Thank you for your very clear explanation.

[@datatab]

Thanks : )

[@aoulipa4165]

Omg, thank you very much. The explanation is clear and easy to understand.

[@datatab]

Glad it was helpful!

[@yuvaraj675]

clear explanation.. thanks for your help ☺️

[@nikiforos6]

Very well explained! Great job!

[@datatab]

Thanks for your feedback, Niki! :-)

[@muhannadal-muhandis1303]

thanks a lot .. you made me understand this lecture very easily

[@FalconFlyer75]

fantastic video, I was struggling a lot with it one thing I would suggest is visually showing how it would all add up to zero to hammer the point in and also i'm assuming that the reason we use squares is to deal with negative numbers?

[@brazhell]

Vielen Dank! Ausgezeichnet Arbeit!

[@imoh5202]

Now I understand better. I think the illustrations made it easier. Thanks

[@datatab]

Great to hear!

[@TheOnlyName]

Ohhh thank you so much, I was supposed to answer questions on this but was never actually taught it. Now it finally makes sense! Thanks :)

[@datatab]

Thanks for your nice feedback! Regards Hannah

[@simpliruchi]

How beautifully and simply explained

[@thefox1703]

Thank you for this excellent tutorial!

[@datatab]

Glad you enjoyed it and thanks for your feedback! Regards Hannah

[@joelmorabang4764]

You earned my subscription! Well explained video .

[@datatab]

Thanks : )

[@allayornasriddinov4256]

Thanks for your good explanation. It’s very very very excellent and easy to understand. Miss love ur explanations.

[@datatab]

So nice of you

[@tyronekim3506]

Thank you for the lesson.

[@berealistic]

Great presentation, thank you

[@Unknown-yl2yv]

OMG this explanation is amazing why I didn't find this video earlier when I was studying Probability and statistics

[@datatab]

Glad it was helpful! : )

[@bdpv025]

The only explanation on youtube I understand thank you

[@datatab]

Many thanks : )

[@karthiknadar8380]

Lot of love to you ma'am so simple explanation ! God bless you !

[@datatab]

It's my pleasure

[@sarahserwar5909]

Exceptionally useful, thank you soooo much

[@datatab]

Glad it was helpful!

[@Roberto-REME]

Great video and very well explained. Your narration was cogent and really well done. And.... you're beautiful. 😊

[@Nothando1]

Thank you so much, this really helped me! ✨

[@datatab]

Many thanks! Regards Hannah

[@dami_wick]

Thank you madam for this great explanation. I tried to remember the formulas but failed. This explanation gave me a better idea about the standard deviation .

[@datatab]

Glad it was helpful!

[@ahmetlacin5748]

I thank you so much ! Great Explanation!

[@datatab]

Thanks for your nice feedback!!!

[@wlsonoma]

I worked for a company that made radiators for 36 years in various jobs. I filled in on one job that made tubes for the radiators. Automatic cutoffs that cut the tubes to length. We would measure 10 consecutive tubes in a row. According to their standard deviation methods if the length bounced back and forth = or- .015 inches from the desired length (the mean) the tubes were fine. If every tube measured .005 inches long, they were bad. I always thought that was so stupid. I think years later they moved away from that but by then I was running a laser and didn't matter to me.

[@124php]

I had to study this a long time ago for statistics. But your explanation with visual content makes it much clear for me. But in the end it became again confusing with variance and standard d.

[@AkifAltundal]

Variation has a different unit (cm^2) compared to the data (cm) or mean (cm). So that's why standard deviation formula has been introduced. Standard deviation has the same unit (cm)

[@yousefmedhat56]

Very clear explanation and helped me a lot, thank you.

[@datatab]

You are welcome! Many thanks for your nice feedback! Regards Hannah