FINALLY! Why we divide by N-1 for Sample Variance and Standard Deviation
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- Опубликовано: 22 авг 2024
- The best and simplest explanation of why we divide the sample variance by n-1. This step-by-step explanation is clear and concise and makes sense! :)
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What would be s^2 if n=1
thank you - watched four videos explaining n-1 and this is the first one that clicked. combination of demonstrating degrees of freedom and explaining the sample mean error helped a lot.
Great vid! From what I gathered, the population mean is predetermined/fixed and no calculation of estimation is needed which would have developed a constraint, leading to all observations contributing to DoF. However, I understand the example at 5:20 is meant to show the significance of each observation on the numerator of population variance, but I think to those who are mathematically inclined see this as a contradiction to the tautology of the sum of (observation minus their mean) = 0 instead of a simple demonstration of the influence each population observation has :)
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
Boy that was a very interesting explanation of degrees of freedom! Thanks!
First of all, thanks for the video. I still don't get, why in the example with the population mean at the end, you said that depending on the value of X4 (10/20/50), the results differ. I mean if you change X4, then also the mean changes and the result will be 0 as for the sample variance or what am I seeing wrong? Thanks for any help :)
These videos are superbly brilliant, THANK YOU!
My search finished here! Thank you!
Excellent! ⭐️
Great explanation of degrees of freedom! Congrats.
For those trying to get a deeper explanation on the matter, try this wikipedia link:
en.wikipedia.org/wiki/Bias_of_an_estimator
Best of luck!
Thanks for the article link!
You didn't fulfil the promise of the title. Ok, the dof is n-1. That doesn't explain why we divide by that quantity.
Wonderful thanks !
Thanks alot...... Such a great information....... 👍
omg you literally saved my life thank you so much!
Literally, eh? I'd love to hear that story.
Thank you v much but my Q is why do u assume that population mean is 10? I mean this assumption is based on what? May be it is not compatible with reality of that population? Actually can we ever measure the mean of weight for instance of a whole population of a country? By the time we are done measuring or entering data of all population probably their weights have changed.
Perfect!! Thank you so much!
Thank you so much man.
Why do we lose just one observation for calculating sample variance? Is it because degree of freedom n-1 in calculating sample mean? Thank you for your answer. I like how you explain stat in layman manner.
+yohanes ronald Because you have to estimate the sample mean. As discussed in the video, estimating the sample mean uses up one observation.
Suppose there are 5 people in a dark room whose positions are unknown. There are 5 unknowns right? But, suppose you are one of the persons, then, to you, there are 4 unknowns. You know where you are (you have been "estimated") and there are only 4 moving parts now.
Now, suppose instead, you and your friend are in the room holding hands. From your point of view, there are only 3 unknowns now. As you and your friend are known (estimated) and there are only 3 moving parts now.
So the number of unknowns (moving parts or degrees of freedom) is dependent on what has to be known before calculating the variance. In this case, you must first calculate the sample mean (so it is known)...so there are only n-1 moving parts now.
Hope this helps
David
+Quant Concepts Smart.
Quant Concepts
wow smart explanations! I get it now. Thanks man and keep up making cool videos!
very helpful! thank you
Using the sample mean will always result in a smaller numerator than using population mean? No, what if the sample mean equals the population mean? (Say the sample is the three numbers 9, 10, and 11.)
Also, the argument of n-1 around 4:24 seems like a bit of hocus-pocus. True, given the sample mean and n-1 of the sample points, you can calculate the last sample point. But getting the sample mean itself did require all n points in the first place! Am I missing something?
I don't understand how sample variance has degrees of variance of n-1: surely if you knew X1, X2, and X3, you wouldn't be able to calculate the variance without knowing X4, and the value X4 took would affect the value of the sample variance?
very nice
Dividing by (n-1) is used for samples; unlike for population.
That is not the question. We are asking about the |b| in n-b. Why b is 1 and not any value like 0
still makes no sense for me. say you have 4 and 2. their mean is 3. technically 4 and 2 do deviate from 3 only by 1. however, any software will tell you 1.41. makes absolutely no sense for me. i have watched like 10 videos and it seems also tutors do not completely understand it.
You're referring to the mean absolute deviation (MAD). Standard deviation is defined differently and does not result in the same values as MAD.
best
What is downward bias?
Always underestimates.
Great
can someone explain me this in a single line...if possible
"one observation does not contain critical input"
So we pretend its not there and divide with n-1 observations but we still take that observation and sum it up in the numerator in the calculation of variance.
That does not make sense.
We divide with n-1 instead of n because we have n-1 observations with critical input, but why does that last observation still go into the sum of squares? Why doesn't the sum in the calculation of variance also ignore one element and goes from 1 to n-1 instead of 1 to n...
This explanation does not make sense.
You may watch this video's explanation: www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/more-standard-deviation/v/another-simulation-giving-evidence-that-n-1-gives-us-an-unbiased-estimate-of-variance
In my case, watching this video and the one from the link has left me pretty convinced. Hope it helps!
@@miskyhusky Alright but that's just a confirmation by doing experiments. This seems like someone did the simulations and said okay we'll use n-1 now but how does that relate to the degrees of freedom. How does the last observation not adding any new information relate to using n-1 in the numerator while still counting the deviation from sample mean for the same observation.
@ThePhysics1234 or @LalitTiwari Did any of you folks happen to get to the bottom of this? I'm all fine with dividing by n-1 cos the nth summation term can be derived from the rest & sample mean; But why do you add this to the numerator?
I am S1 who is doing this :/
I give up. Maybe it requires much more math & longer tutorials to understand why it's (n-1)
Hi, check this link for a more deep explanation:
en.wikipedia.org/wiki/Bias_of_an_estimator
😂😂😂
RIP sample variance !
Why using the sample mean will always result in a smaller numerator than using population mean? Orh I get it! Because the sample mean will always be closer to the sets of numbers. WTF! cool :D
+John Lewis :)
One property you mentions at 3.55 will hold true for any mean .. be it sample mean or population mean .. I dont follow how does it reduce 1 DoF only for sample and not for population. If you can explain that will be great. Thanks
Coll
So wait, a sample can never *underestimate* a population mean?
"always result in a smaller numerator"? I'm crazy or this is a lie. if you not divide by n-1 you'll get a different result, ok, but it's not the point here. why you said that? I think it's the point for me to understand it. Is this n-1 not better for predict variation from mean of samples that you really find the population mean possible to calculate? Imagine a case you don't know the population mean, how would you say there's some degree of freedom if you have not even noticed that the first or last observation. Ok , if we are dealing with last observation we are not dealing with statistics.. but the doubt is still the same... why you said that? Maybe i answered this question inside my brain but I really wanna be sure