Variance and standard deviation are both measures of how spread out a set of data points are, but they differ in how they express this spread. Variance is like the average of how far each data point is from the mean (the average). It tells you how much the data points vary or spread out from the average. If the variance is large, it means the data points are spread out widely from the average. If it's small, the data points are closer to the average. Standard deviation is simply the square root of the variance. It's essentially a measure of how much the data points deviate from the mean. So, if the standard deviation is large, it means there's a lot of variability among the data points. If it's small, the data points are more clustered around the mean. Think of it like this: variance gives you a measure of spread, but in the same units as the data (for example, if you're measuring length, the variance would be in square units). Standard deviation is more interpretable because it's in the same units as the original data, making it easier to understand how spread out the data is.
You have not only explained the Standard Deviation calculation in an easier manner with an example but also answered the common questions about Arithmetic mean and Quadratic mean. Thank you for the great video.
I understood everything except one point Why in calculating the standard deviation of a sample we divide the mean be n minus one I mean this make it more accurate to represent the population ? why not just divide it by n alone ? Why exactly minus one ? Not minus 2 or plus one for example?
Vielen Dank für eure tollen Videos! Ihr erklärt das Thema Statistik sehr verständlich und auf eine angenehme Weise. Könntet ihr (ähnlich wie zur Standardabweichung) auch ein Video zum Standardfehler des Mittelwertes machen?
is there a relationship (or a rule of thumb) of how big the sample size "n" should be at minimum to be confident that it wont change the standard deviation much for bigger sample sizes?
Hi, this is a bit complicated but I will try. When calculating the standard deviation for a sample, it is divided by (n - 1) instead of (n) to correct for bias and get a better estimate of the population standard deviation. This adjustment is known as "Bessel's correction." Here's why it is done: 1. Population vs. Sample: - If you have a complete population, you would use (n) (where (n) is the total number of data points) to calculate the standard deviation. - In the case of a sample, which is a subset of the population, using (n) would typically underestimate the population standard deviation because the sample might not fully represent the population's variation. 2. Bessel's Correction: - By dividing by (n - 1), you adjust for this underestimation. The denominator (n - 1) provides a more accurate estimate by accounting for the "loss" of degrees of freedom due to the mean being derived from the sample itself. - In simpler terms, when you use a sample to estimate the population standard deviation, you effectively "lose" one data point's worth of information due to calculating the sample mean. Dividing by (n - 1) compensates for this. 3. Degrees of Freedom: - The use of (n - 1) is linked to the concept of degrees of freedom. When you estimate a parameter from the data (like the sample mean), you reduce the degrees of freedom because the sample values are constrained by this estimate. Dividing by (n - 1) corrects for this loss, providing a less biased estimate of variability. By using (n - 1) instead of (n), the calculated standard deviation from a sample more closely approximates the true standard deviation of the population, especially when the sample size is small. Regards Hannah
Literally was lost, mainly because my professor goes fast and I cant catch up with what he says but holy am I grateful for this video. I understand most but this just help clarified what I am learning by a significant amount!!
Die Stimme ist unangenehm anzuhören. Der Inhalt ist wirklich nützlich. Gerne mehr :) Gerne bei zukünftigen Videos nicht so überheftig betonen und auch die Sprachmodulation etwas reduzieren. So hatte ich das Gefühl, dass die Stimme glaubt, dass ich ein Vollidiot bin, der die Sprache nicht spricht.
Hi vielen danke für dein Feedback! Das Mikrofon war diesmal leider ein wenig Laut eingestellt, daher ist es teils ein wenig hoch/kwitchig. Der Rest ist denke ich Geschmackssache und da es aktuell recht gut ankommt werden wir den weg erstmal so weiter gehen. Wie man hört : ) sind wir keine ausgebildeten Sprecher und keine natives, aber das muss bei einem RUclips-Kanal ja auch nicht sein : ) Das gleiche Video gibt es auch nochmal auf deutsch auf unserem deutschen Kanal: ruclips.net/video/aR1cX9abjag/видео.html LG Mathias
If I pull a card to try for the ace of spades (1/52 chance) and I win $500 each time I do, and $0 all the other times, how do I calculate the variance? each pull would be 1/52 (not 1/52 then 1/51 then 1/50...)
If you like, please find our e-Book here: datatab.net/statistics-book 😎
Variance and standard deviation are both measures of how spread out a set of data points are, but they differ in how they express this spread.
Variance is like the average of how far each data point is from the mean (the average). It tells you how much the data points vary or spread out from the average. If the variance is large, it means the data points are spread out widely from the average. If it's small, the data points are closer to the average.
Standard deviation is simply the square root of the variance. It's essentially a measure of how much the data points deviate from the mean. So, if the standard deviation is large, it means there's a lot of variability among the data points. If it's small, the data points are more clustered around the mean.
Think of it like this: variance gives you a measure of spread, but in the same units as the data (for example, if you're measuring length, the variance would be in square units). Standard deviation is more interpretable because it's in the same units as the original data, making it easier to understand how spread out the data is.
You have not only explained the Standard Deviation calculation in an easier manner with an example but also answered the common questions about Arithmetic mean and Quadratic mean. Thank you for the great video.
This is by far the simplest and clearest explanation I found thank you!
Glad it was helpful! Regards, Hannah
I understood everything except one point
Why in calculating the standard deviation of a sample we divide the mean be n minus one
I mean this make it more accurate to represent the population ? why not just divide it by n alone ? Why exactly minus one ? Not minus 2 or plus one for example?
Thanks a lot for explaining it so clearly and slowly. Most videos go too fast and I have to pause all the time, but with you it was perfect!
Glad it helped and thanks for your nice feedback! Regards Hannah
U r the best i finally found someone who can explain this clearly with examples
Great programming and you do a fantastic job of explaining. Plus, I think you’re beautiful.
Thank you very nicely explained.
Just love it, thanks!
Many thanks : )
this one is more clear explanation
very clear explanation with visual and speak slowly so we can catch every steps, thanks subscribed!!!
Glad it was helpful and many thanks for your feedback! Regards Hannah
But why we use standard deviation instead of average deviation do not explained in this video
Great Lecture, thank you so much.
Math bless you.
Vielen Dank für eure tollen Videos!
Ihr erklärt das Thema Statistik sehr verständlich und auf eine angenehme Weise.
Könntet ihr (ähnlich wie zur Standardabweichung) auch ein Video zum Standardfehler des Mittelwertes machen?
Hier auch vielen Dank nochmal : )
great explantion 👏🏻
Glad it was helpful!
Well explained🤝🏻
Glad you liked it
One of the best videos on SD & Variance, thanks a ton for keeping things simple.
Is datatab free to use?
Can't u just try
niec explaine
Thanks : )
Thank you so much!!! This was so helpful :)
You're so welcome!
😊nice
Excellent.
Many thanks : )
this helped a lot. thank for the explaination
You are welcome!
so clear
Very well explained ❤
is there a relationship (or a rule of thumb) of how big the sample size "n" should be at minimum to be confident that it wont change the standard deviation much for bigger sample sizes?
by adding 10 of each, var and std will remain same?
Thank you so much for explaining these terms as simple as possible.
i really have to thank you for this explanation :)
Amazing video thank you for sharing this information.
hello i am a bit confused after summing it up and divide by 6 i got 132 will you got 11.5 at 2:33 in the video please any one can help
The last step is that you need to calculate the square root of 132 which will get you to 11.5
Powerful
Why n -1 tho? (Why it has to be -1?)
Hi, this is a bit complicated but I will try.
When calculating the standard deviation for a sample, it is divided by (n - 1) instead of (n) to correct for bias and get a better estimate of the population standard deviation. This adjustment is known as "Bessel's correction."
Here's why it is done:
1. Population vs. Sample:
- If you have a complete population, you would use (n) (where (n) is the total number of data points) to calculate the standard deviation.
- In the case of a sample, which is a subset of the population, using (n) would typically underestimate the population standard deviation because the sample might not fully represent the population's variation.
2. Bessel's Correction:
- By dividing by (n - 1), you adjust for this underestimation. The denominator (n - 1) provides a more accurate estimate by accounting for the "loss" of degrees of freedom due to the mean being derived from the sample itself.
- In simpler terms, when you use a sample to estimate the population standard deviation, you effectively "lose" one data point's worth of information due to calculating the sample mean. Dividing by (n - 1) compensates for this.
3. Degrees of Freedom:
- The use of (n - 1) is linked to the concept of degrees of freedom. When you estimate a parameter from the data (like the sample mean), you reduce the degrees of freedom because the sample values are constrained by this estimate. Dividing by (n - 1) corrects for this loss, providing a less biased estimate of variability.
By using (n - 1) instead of (n), the calculated standard deviation from a sample more closely approximates the true standard deviation of the population, especially when the sample size is small.
Regards Hannah
@@datatab But why specifically n-1 and not possibly something even higher like n - 10, etc?
Good explanation
Thanks and welcome, Regerds Hannah
Gracias Hannah!
You are welcome Daniel : )
divided by n or n-1??
It depends on the situation!
That is amazing! Thanks
Literally was lost, mainly because my professor goes fast and I cant catch up with what he says but holy am I grateful for this video. I understand most but this just help clarified what I am learning by a significant amount!!
Excellent
thank you!
excellent explanation
👍👍👍
The best explanation of standard deviation ever. For the first time, I have a full understanding of SD. Thank you so much
Die Stimme ist unangenehm anzuhören. Der Inhalt ist wirklich nützlich. Gerne mehr :)
Gerne bei zukünftigen Videos nicht so überheftig betonen und auch die Sprachmodulation etwas reduzieren.
So hatte ich das Gefühl, dass die Stimme glaubt, dass ich ein Vollidiot bin, der die Sprache nicht spricht.
Hi vielen danke für dein Feedback! Das Mikrofon war diesmal leider ein wenig Laut eingestellt, daher ist es teils ein wenig hoch/kwitchig. Der Rest ist denke ich Geschmackssache und da es aktuell recht gut ankommt werden wir den weg erstmal so weiter gehen. Wie man hört : ) sind wir keine ausgebildeten Sprecher und keine natives, aber das muss bei einem RUclips-Kanal ja auch nicht sein : ) Das gleiche Video gibt es auch nochmal auf deutsch auf unserem deutschen Kanal: ruclips.net/video/aR1cX9abjag/видео.html LG Mathias
The voice helps me a lot actually. And the fact that you speak slowly also. So thank you. 🙏🏻
If I pull a card to try for the ace of spades (1/52 chance) and I win $500 each time I do, and $0 all the other times, how do I calculate the variance? each pull would be 1/52 (not 1/52 then 1/51 then 1/50...)
I know how, but I wont tell you
Great video thanks