Why do we divide by n-1 and not n? | shown with a simple example | variance and sd

If you like to see the mathematical proof of why we divide by n-1, have a look at this video:
• Why we divide by n-1 w...
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In this video, we will see why we need to divide by n-1 to get an unbiased estimate of the population variance. We will use simple simulated data to understand this (no advanced math). At the end of the video, we will see that the sample standard deviation is a biased estimate.

[@tilestats]

If you like to see the mathematical proof of why we divide by n-1, have a look at this video: kzbin.info/www/bejne/eJ7apaywbMylp80

[@merveak1129]

I'm a statistics student and I always wonder why we should divide by n-1. This video is very helpful in understanding the philosophy of statistics. Thank you very much for making this video and enlightening our brains and questions.

[@sakkariyaibrahim2650]

most convincing demonstration on this issue, so far. Great

[@jimbobur]

I came across this video looking for the 'tons of maths' behind the proof for using n-1. Wikipedia's 4 lines of algebra on it are almost harder to follow than a hand-waving explanation.

[@anthnyalxndr]

@TileStats for those not familiar with writing code, it may be useful to make a video demonstrating how you actually create these simulations using Python, R, or whatever you use. Similar to you, I sometimes find that I need to run a Monte Carlo simulation to understand a concept and trust that it actually works out as intended.

[@tilestats]

Thanks for your suggestion. I will try to do that in the future.

[@logansmith7719]

Great explanation. Very helpful

[@KonradGebura]

Hello, great video! I just have one question, why don’t we do n-2 or n-3? I get the degree of freedom idea but I don’t understand why degrees of freedom relate to the final calculation. Is this the result of trial and error to find the correct constant to subtract by?

[@tilestats]

In the beginning of the video I mention that you can show mathematically why we divide by n-1. I would recommend this video that show that kzbin.info/www/bejne/emLLmJx3ocZmgas

[@KonradGebura]

@@tilestats Thank you for the recommendation! I now understand the logic behind the equation thanks to your video, as well as the proof for the constant being exactly -1.

[@muhtorbekmuratov9430]

Awesome video !

[@file4318]

Thank you very much for your video, it was very very good at explaining. But I have one more question, If descriptive statistics do not try to generalize to a population (since there is no uncertainty in descriptive statistics), then why does the sample standard deviation try to best estimate the population mean? Yet it is still considered a descriptive statistic

[@tilestats]

The sample variance tries to estimate the population variance, which is best done by n-1 if we need to estimate the mean from the sample. The interval "mean +/- 1 SD" can be interpreted as it is expected to include approximately 68% of the data points, which does not hold if you divide by n instead or n-1 for small sample sizes.

[@moktatafatforyou-2378]

Thank you great vedio

[@booni5114]

Thank for the great video, but why (at 7:42) do we lose one degree of freedom?

[@tilestats]

Because you estimate one parameter (the mean) in order to calculate the variance.

[@anilkumarsharma8901]

how many formulas in total statics so we found out something as constantant source of income

[@mfayed73]

Hi, I thought that we divide to n-1 because if we measure variance between 2 points one of them is the SD and the other a normal point the this means we have 1 room or 1 shaded area that we measure the variance ...meaning if we have 2 points then we have 1 area ...3 points then 2 areas ...where the area represents the variance between the 2 points .... so we end up n-1 #of areas when n is #of points

[@duckface8425]

I heard something about degrees of freedom

[@anilkumarsharma8901]

Which country??

[@TheJuliusCo]

I studied quantum mechanics, its the same principle, any ways students should be able to demstrate variance at any time, dont make math less

[@MrConverse]

1:30, the point representing 172 is too far to the right. It’s much closer to 175 than 172. Minor error but perhaps it will help someone avoid confusion.

[@comments94]

Why n-1 and not n-2 then?

[@tilestats]

There is a similar question below or above where I answered this.

[@FunctionalEfficientDesign]

L.