Why Sample Variance is Divided by n-1

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[@binarystar4947]

I came here by searching the ans to this question from your live day 2 - basic to intermediate statistics video and got my ans ✨

[@bankimdas9517]

Dividing by 'n' underestimates the true variance so to correct the bias we use (n-1) in denominator.

[@sumangupta871]

What happen if someone choose 5 samples from the right. Why we are not dividing by n+1 in that case?

[@bharratkhanna6096]

The exact reason is bias introduced by sample mean since it is an estimated value of population mean and because sum of deviations should be 0, hence this constraint restricts the freedom of data points, hence to counter the bias and constraints introduced we use n-1, remember sample variance is unbiased but sample std deviate still is biased because of concave functionality of square root introducing a negative bias and n-1 is a linear function which fails to correct sample std to a level as good as sample variance. Remember this is not experiment this is mathematically proved and Bessel correction(n-1) is not used when population mean is present.

[@DoingMyIkigai]

wasted 10 mins of life ---- not exzact reason given

[@kumudsharma007]

Cris please remove this video as soon as possible if you want save your reputation. This is completely teaching students very wrong concept.

[@Ezio-ft8zm]

poonam kumari se irritate hogya tha and so i landed up here before my stats exam ! feels so good to learn a concept which i didnt even understand after listening two times in a 45 min class !

[@gunjanagrawal8626]

This could be understood well from the simulation video used by the Khan Academy.

[@arnabghosh2818]

Theoritically in core statistics there is another justification related to degrees of freedom.

[@dipayanbhadra8332]

"Researchers experimented and saw n-1 gives good estimates"- I am not satisfied with this explanation. If this were an interview question, would the interviewer be happy with this and? Poor explanation.

[@abhinandandey_ricky]

n-1 is actually degree of freedom

[@user-yd3zk4hb1o]

Answer :

[@abcefg7045]

if we take right-skewed data, then dividing with n - 1 will create more difference ?

[@sudiptasen634]

Hi Krish, Thank you for helping us to understand the concept. I had one question.

[@snehalhon]

After watching each video lecture of your sir ....i m getting my concept more clear ...no words for you ...u r great

[@pratikmanghwani7417]

With all due respect you should explain why it is unbiased with the math behind it. Thanks

[@thevoiceofdarkness7655]

This may be a silly question, but why do we assume it is more likely for my sample to be skewed below the mean than above?

[@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

[@snehaagarwal7640]

but what if we take the data on the right side of population variance and divide that by n-1...that will be inaccurate then

[@modemnaveen6240]

According to logic explained in this video , the sample mean and population mean can be different based on samples we are picking right ? So why we are just under estimating variance . Why not mean ? Can some one please explain