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 😎
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.
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
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.😈
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.
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.
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.
Ma'am, you are awesome. The simplicity exeh! Usually people come to UA-cam 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!
it's a bit embarrassing to admit, but as an engineering student, thank goodness for this video! i always have such a hard time w these topics and I can't believe I FINALLY understood what this means! Thank you so much 😭❤
Perfectly explained - clear and to the point! Thank you for addressing my internal question that standard deviation, as an "average", is more than just the mean!
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.
after 15 years that I studied math and used it in various scenarios this video finally make me understand the importance of the std. thanks, it was the best 7 minute math learning of my life.
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!
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 🙏🙏
Thank you mam, thank you thank you. I am just in class 10th and an AI student. This concept was just out of my mind. But now it is just crystal clear!!!!
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.
Excellent presentation, clear and concise. The only thing I miss is an explanation of WHY the standard deviation of a sample is divided over "n-1", as opposed to dividing over "n" as is the case for the whole population. This is something I've never quite understood.
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! 😭❤️
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
There were two things you should mention in your tutorial: 1. Standard deviation is +/- because you are taking the square root of the variance. 2. You should explain why n-1 i.e. the concept of degrees of freedom. Since you calculate the mean from the sample, you lost one degree of freedom thus n-1, instead of n. For large sample size (30 or so),the difference between the two is minimal. Dr. Ajit Thakur (USA)
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.
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 .
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.
Hi from Malaysia, thank you very much for simple and clear explanation and it is easy to understand. Btw, i keep on screaming "Get To The Choppa!" inside my head while listening to your explanation 😅. But no worries your explanation is great! I hope I can learn more from your channel 🤣
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?
Your explanation is beautiful. However a couple of sentences on the following would have been great 1. Quadratic mean is used in SD, why not just arithmetic mean 2. Why divide by n-1 instead of n when working with samples 3. Significance of varience
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.
@@jdoesmath2065 Thanks, but what exactly? I asked at least 3 questions, so it's rather difficult to match your answer. And if what you mean is taking the derivative, what does it have to do with anything? Why all of a suddent we need to take the derivative? I know it's fun, and for that reason we could as well do integration, but will it give us any practical information?
@@piotrrybka318 Sorry, I was referring to the question about the standard deviation and why we square the differences instead of using the absolute value. The squaring function is differentiable whereas the absolute value function is not. Behind the formulas we use in elementary statistics is a lot of calculus.
2 Questions: 1. 3:57 If we are just worried about sum being 0, why don't we just absolutize the values? 2. 5:50 How minus 1 justifies this? Why not minus 2, 3, 4 or even divide them?
Nice and easily explained, but I have used two methods for calculating the standard deviation (the above being one of them), and both come to 11.50 and not 12.06.
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.
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?
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.
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.
Thank you! 1) You explained, which method (N vs N-1) I have to use in which situation. But I didn't understand, why. 2) when "standard deviation" means the "mean value of all deviations": why I have to square the differences?
😄You answered a question I've always had, but never looked into it. Why the heck do you square the deviations to find the mean and then take the root of that, which is not really the correct average? You said, "If the arithmetic mean would be used it would be zero everytime". Hadn't looked into that. Now this provokes a new question: Why then not just take the average of the absolute value of the deviations? That would prevent the always zero result.
Many thanks for the nice feedback!!! I have just learned that there is a name for the metric you mentioned, it is called average absolute deviation. en.wikipedia.org/wiki/Average_absolute_deviation However, it seems that the standard deviation has become more accepted! Maybe also because of the variance, if the variance occurs in an equation, it is easier to continue calculating with it, it is easy to form the derivative and so on. Regards Hannah
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 😎
How did you get 11.50 please?
@@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
@@ajsanpedro If we use 6, the result is 11.5. Thank you!
The way you say "Standard Deviation" is so cute
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
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 :)
Many thanks for your Feedback! Actually I am from Austria : ) Regards, Hannah
Very well explained
There was a time when Austria was within the standard deviation of Southern Germany!
😅
😂
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.
True. You said it. 👏
I don't understand why anyone would height this video. That was very clearly explained. Thanks!
LMAO
AHAHAHHAHAHAHAHA
BRUH
you rascal :D
took me a second ... almost died laughing!
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
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.😈
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!
Many thanks : ) Regards Hannah
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
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.
@@purplecrayon7281 I’m in the UK but yes we have to study it
Do you have any interest in research methodology and psychoanalysis?
Clarity and pace of your voice is making it very easy to understand.
Thanks : )
It's a bold social experiment to calculate the standard deviation of hate. I salute you.
Yes a little embarrassing, but you never stop learning : )
Hate is a mean value
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.
Hoe many languages do you speak?
@@datatabThat Austrian accent is actually adorable 🥰. Great explanation of the concepts as well!
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.
Would have at least been useful to have mentioned the name 'Bessel's Correction' in case anybody wanted to read further.
Ma'am, you are awesome. The simplicity exeh!
Usually people come to UA-cam 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!
Thank you so much 🙂
it's a bit embarrassing to admit, but as an engineering student, thank goodness for this video! i always have such a hard time w these topics and I can't believe I FINALLY understood what this means! Thank you so much 😭❤
Glad it was helpful and thanks for your nice Feedback! Regards Hannah & Mathias
Perfectly explained - clear and to the point! Thank you for addressing my internal question that standard deviation, as an "average", is more than just the mean!
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.
0:40 "Let's say you measure the hate of a small group of people" - I've done it many times, mostly by accident.
You have explained very clearly and slowly to make understand us! Thank you a lot! 👍
Hands down the best and most succinct explanation of std dev I've ever seen.
This is the first time I ever understand the concept of standard deviation and its purpose. Thank you so much for this helpful content!
after 15 years that I studied math and used it in various scenarios this video finally make me understand the importance of the std. thanks, it was the best 7 minute math learning of my life.
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.
It's her accent not your hearing. Felt same fffs
They measure hate 😂
@@SprakanaKerum haha same, fr I also thought measuring hate, Lmao
Me too I thought she was trying to be quirky or something.😂
one of the best-detailed example, I have ever seen....i dint think I will ever forget this
Many many thanks!!!!! Regards, Hannah
You have explained very clearly and slowly.
Such a simple explanation.
Keep up the good work! Cheers!
Thank you a lot!
Thanks for the simple but profound delivery of content that is understandable to anyone. Keep going. Congrats
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!
Many thanks for your nice Feedback!!! Regards Hannah
Such a simple explanation. Love it when people who knows stuff explain things.
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 🙏🙏
Thank you mam, thank you thank you. I am just in class 10th and an AI student. This concept was just out of my mind. But now it is just crystal clear!!!!
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.
Oh thanks! I did not notice that : ) In the current situation hate would even fit : ( Regards Hannah
Lovely explanation. 7 min video saved many hours.
Glad it was helpful! Regards Hannah
A beautiful lady explaining conceptual topic beautifully... thankyou ❤....now I understood the concept
Finally I'm able to actually understand this thing after years. Very well explained indeed! ❤
Excellent presentation, clear and concise. The only thing I miss is an explanation of WHY the standard deviation of a sample is divided over "n-1", as opposed to dividing over "n" as is the case for the whole population. This is something I've never quite understood.
Have u understood?
Short and sweet explanation. I'll never forget standard deviation, variance and its formula.
Thanks!
Thank you for your amazing videos! True help to the people who struggle with numbers, but need it in their professions. Greetings from Lithuania!
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! 😭❤️
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
Many thanks!
As an online college student, I have some problems with this. This helps me to understand and thank you so much.
Thanks!
It really helps me to grasp topics when they are simply explained which you did. Thank you.
Glad it was helpful!
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
New subscriber here from the Philippines. Thank you for your very clear explanation.
Thanks : )
There were two things you should mention in your tutorial:
1. Standard deviation is +/- because you are taking the square root of the variance.
2. You should explain why n-1 i.e. the concept of degrees of freedom. Since you calculate the mean from the sample, you lost one degree of freedom thus n-1, instead of n. For large sample size (30 or so),the difference between the two is minimal. Dr. Ajit Thakur (USA)
Thank you for this , was stuck. Sending love from South Sudan,Africa !!
You are so welcome!
This was really informative and easy to understand. You earned a subscriber today! Thank you
Awesome, thank you!
Thank you for a clear and nice paced video. I have watched others on this subject and yours is the best by far. 👍
Wow! So concise and clear. Visuals helped too.
Thanks!!😊
Keep up the good work! Cheers!
Absolutely no idea why this showed up in my feed, but I am glad it did. Thank you for the succinct explanation.
i have to prepare for may major exams and research . i paid high fees. and now learning from you
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.
This is excellent. Thanks for your help in educating our world about such important things.
3 weeks of my college in 7 minute
Thank you very much
Most welcome 😊 And thanks for the nice feedback : )
Thank you loads for this video!! The really complicated formula in my text book looked like a rocket science 😭 I finally get it now
You just helped me pass my finals🙏🙏
Geate! Thanks for your feedback!
The explanation is on point and easy to understand. Thank you DATAtab :)
Many thanks for watching and for the feedback! Regards, Hannah and Mathias
Very well explained, finally understood why Standard Deviation is important. Thank you so much 🙏👌
Happy to help
Your smile makes this look so easy. Thanks a lot!
My pleasure 😊
I remember in 80’s my Maths teacher who was a terror ; We simply learnt out of fear ; This video makes learning damn easy
Wow! I had statistics in 1967 at Penn State and it was way too intense for my intellect. You made this so understandable, thank you greatly.
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 .
Glad it was helpful!
Thankful for your clear explanation
Crystal clear now ❤
Thank you again and again❤
Finally I got to understand what the std deviation is! Great video
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.
Happy to help : ) Regards Hannah
Thank you for taking the time to make this video. Much appreciated.
Thank you for the clarity as to standard deviation. You are the best!
Happy to help!
Please do not stop posting your videos. Very helpful. Other creators stopped.
This video really helped me to understand the concept of standard deviation. Specially the example. Thank you so much!🤗
Hi from Malaysia, thank you very much for simple and clear explanation and it is easy to understand. Btw, i keep on screaming "Get To The Choppa!" inside my head while listening to your explanation 😅. But no worries your explanation is great! I hope I can learn more from your channel 🤣
Such a simple explanation, thank you!
You're welcome! Many thanks for your nice feedback! Regards, Hannah
If only this was explained as you did, when i was at school.... Very well presented. Thank you
Something to thank you for - an education...
and that's exactly what I'll do...Thank you!
Thank you so much : ) Regards Hannah
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 :)
Thanks for your nice feedback! Regards Hannah
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.
Happy to help! Thanks for you nice feedback! Regards Hannah
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?
THANKS SO MUCH FOR THIS!! Now it all makes sense spectacularly for me. Cannot thank you enough.
Your explanation is beautiful.
However a couple of sentences on the following would have been great
1. Quadratic mean is used in SD, why not just arithmetic mean
2. Why divide by n-1 instead of n when working with samples
3. Significance of varience
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.
I also tried ti understand these points without success...😒
It’s about differentiability.
@@jdoesmath2065 Thanks, but what exactly? I asked at least 3 questions, so it's rather difficult to match your answer. And if what you mean is taking the derivative, what does it have to do with anything? Why all of a suddent we need to take the derivative? I know it's fun, and for that reason we could as well do integration, but will it give us any practical information?
@@piotrrybka318 Sorry, I was referring to the question about the standard deviation and why we square the differences instead of using the absolute value. The squaring function is differentiable whereas the absolute value function is not. Behind the formulas we use in elementary statistics is a lot of calculus.
Now I understand better. I think the illustrations made it easier. Thanks
Great to hear!
This is a very clear and easy explanation of standard deviation.thanks
The only explanation on youtube I understand thank you
Many thanks : )
Amazing way of teaching! I love your explanations.
Many thanks : ) Regards Hannah
You explained in one video that took me years to understand to get a MSC.
2 Questions:
1. 3:57 If we are just worried about sum being 0, why don't we just absolutize the values?
2. 5:50 How minus 1 justifies this? Why not minus 2, 3, 4 or even divide them?
Thank you so much! I am a simpleton so this really helped me
Thanks for your feedback!!! Regards Hannah
I just came back to like this video, it's the best I've ever seen
Many thanks!!!
Nice and easily explained, but I have used two methods for calculating the standard deviation (the above being one of them), and both come to 11.50 and not 12.06.
Hi miss, I am glad that I found you . Thank you so much for teaching us .This really helped us
excellent presentation in a very simple and digestible way. thank you
Glad it was helpful!
you have such a sweet voice 🌹☺️
Great video and very well explained. Your narration was cogent and really well done. And.... you're beautiful. 😊
Simple and clear explanation....
Thank you❤
Glad it was helpful! Thanks for your nice feedback! Regards Hannah
Very well explained! Great job!. Thank you for taking the time to make this video. Much appreciated..
Lot of love to you ma'am so simple explanation ! God bless you !
It's my pleasure
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.
This is exactly what occurred to me after watching, please elaborate on that dear author.
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?
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.
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.
@@KT-dj4iy Wow! That is quite a lot of detailed information, which I appreciate. Thanks for all of your work on this topic. It is very helpful.
Thanks for your good explanation. It’s very very very excellent and easy to understand. Miss love ur explanations.
So nice of you
Thank you for smooth teaching
You are welcome! : )
Thank you! 1) You explained, which method (N vs N-1) I have to use in which situation. But I didn't understand, why. 2) when "standard deviation" means the "mean value of all deviations": why I have to square the differences?
great way of teaching. Love this video
Glad you liked it!
Omg, thank you very much. The explanation is clear and easy to understand.
Glad it was helpful!
😄You answered a question I've always had, but never looked into it. Why the heck do you square the deviations to find the mean and then take the root of that, which is not really the correct average? You said, "If the arithmetic mean would be used it would be zero everytime". Hadn't looked into that.
Now this provokes a new question: Why then not just take the average of the absolute value of the deviations? That would prevent the always zero result.
Many thanks for the nice feedback!!! I have just learned that there is a name for the metric you mentioned, it is called average absolute deviation. en.wikipedia.org/wiki/Average_absolute_deviation However, it seems that the standard deviation has become more accepted! Maybe also because of the variance, if the variance occurs in an equation, it is easier to continue calculating with it, it is easy to form the derivative and so on. Regards Hannah
Somewhere I read, it adds little more accuracy as the root of the squared mean will be little different from modulus mean.
Gracias por tan importante explicación ❤
Thanks : ) Regards Hannah
Exceptionally useful, thank you soooo much
Glad it was helpful!
excellent presentation in a very simple and digestible way. thank you. thank you from my heart since you simplified it so much .