In this video we discuss why and when we divide by n-1 instead of n in the sample variance and the sample standard deviation formula, known in the statistics literature as the Bessel's correction. This method corrects the bias in the estimation of the population variance. but only partially corrects the bias in the estimation of the population standard deviation (and that's why I didn't include the standard deviation in this video).
*References*
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Expected value of sample variance proof: https://proofwiki.org/wiki/Bias_of_Sample_Variance
*Related Videos*
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Why neural networks are universal functions approximators: https://youtu.be/O45AaRPQhuI
Bagging vs Boosting: https://youtu.be/tjy0yL1rRRU
Why we need activations in neural nets: https://youtu.be/rj6K46u0J5w
Bias variance Trade-off: https://youtu.be/5mbX6ITznHk
Neural networks on tabular data: https://youtu.be/e62CBva4TYc
*Contents*
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00:00 - Intro
00:19 - Population vs Sample Statistics
01:22 - Population vs Sample Biased Variance Example
02:13 - Expected Value of the Biased Variance
03:34 - Bias Source Intuition
04:38 - Degrees of Freedom
05:55 - Outro
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#variance #standarddeviation #bias #statistics