Good job over all! One thing i was hoping you'd explain is why we square the variance instead of taking the absolute values. I think it's a natural question i get sometimes from my students (I do research in math finance in variance and volatilty swaps). For anyone curious there's a lot of reasons why but one of the more accessible reasons is that we want to punish data points that stray very far away from the mean disproportionately. This is because a dataset that has 10 data points 1% from the mean should have less variance than one with 1 datapoint 10% from the mean. Squaring does this for us.
Good point, but then, why not using a power of 4 or 6? It would also avoid the sign problem and would penalize the outliers even more than a power of 2. I guess it is a compromise but then the explanation turns too subjective IMO. I usually tell another story to justify using squares instead of absolute values. By using squares the formula look a lot like an euclidean distance, which sparks a deeper connection with geometry. I know this might seem too abstract for some students but if you conceptualize your dataset as a single point in a space that has as much dimensions as observations there are, then looking for how your data varies is just looking for the euclidean distance between the point representing your whole dataset and a point whose coordinates represent the average of your dataset. And euclidean distance gives an intuitive way of understanding variance: Variance is what separates your datapoints from the average of the dataset.
Very nice video, but you should mention why we square difference between mean and value instead of for example taking absolute value which seems to be more natural than squaring. If we would just want values to be positive we could as well take 4th power
2:03 You could have added that using the average as the 'base point' gives the least possible value for variance. Why not use the maximum? Because that would be infinity and not be useful hence
I think you’re wrong at the end because sqrt isn’t linear. The average distance from the mean would use absolute value and summing and would be different from squaring summing then rooting
mixed feelings... genuine attempt to add value, missed a few points, e.g. why square instead of use abs values. "went off track" needs more justification. "explained it so well" is just another shill.
Good topic for you should be how people lie using statistics, applications of calculus, or iff you have a lot more knowledge then talk about the millennial problems😅
Good job over all! One thing i was hoping you'd explain is why we square the variance instead of taking the absolute values. I think it's a natural question i get sometimes from my students (I do research in math finance in variance and volatilty swaps).
For anyone curious there's a lot of reasons why but one of the more accessible reasons is that we want to punish data points that stray very far away from the mean disproportionately. This is because a dataset that has 10 data points 1% from the mean should have less variance than one with 1 datapoint 10% from the mean. Squaring does this for us.
Thanks @RomanNumural9, I will teach that to my own students from now on!
Good point, but then, why not using a power of 4 or 6? It would also avoid the sign problem and would penalize the outliers even more than a power of 2. I guess it is a compromise but then the explanation turns too subjective IMO.
I usually tell another story to justify using squares instead of absolute values. By using squares the formula look a lot like an euclidean distance, which sparks a deeper connection with geometry. I know this might seem too abstract for some students but if you conceptualize your dataset as a single point in a space that has as much dimensions as observations there are, then looking for how your data varies is just looking for the euclidean distance between the point representing your whole dataset and a point whose coordinates represent the average of your dataset. And euclidean distance gives an intuitive way of understanding variance: Variance is what separates your datapoints from the average of the dataset.
Here before the channel blows up. Keep up the quality.
Thanks!
this is the proper explanation!
Great explanation man, keep it up, went through major channels to explain it, failed, here totally understood it. Thanks a lot
You're a legend!
Very nice video, but you should mention why we square difference between mean and value instead of for example taking absolute value which seems to be more natural than squaring. If we would just want values to be positive we could as well take 4th power
New favourite channel!
2:56 Why not take the absolute value instead? Wouldn't it result in a more accurate value?
Great content. Keep up with the good work :)
2:03 You could have added that using the average as the 'base point' gives the least possible value for variance. Why not use the maximum? Because that would be infinity and not be useful hence
its the moment of inertia of a data set
I think you’re wrong at the end because sqrt isn’t linear. The average distance from the mean would use absolute value and summing and would be different from squaring summing then rooting
Variance is the square of standard deviation calculating how far the results deviate from the mean
Thanks for the vid
kill the Background music entirely..
The video was promising to begin with...then went off track.
Understood, will work on it next time. Thanks for the feedback!
What are you talking about he explained it so well and didnt go off point
mixed feelings... genuine attempt to add value, missed a few points, e.g. why square instead of use abs values.
"went off track" needs more justification.
"explained it so well" is just another shill.
@@mrbatweed bro chill its a fucking math video not your moms sex tape
@@mrbatweedwell we don’t use abs value as that makes calculations much harder. You can use it, but using squares is just a whole lot easier.
Good topic for you should be how people lie using statistics, applications of calculus, or iff you have a lot more knowledge then talk about the millennial problems😅