Why Standard Deviation Divides by n−1

Standard deviation is the square root of the average squared distance from the mean, and this video builds it out of squares you can see, with one small dataset worked by hand. Then it shows square by square why the sample version divides by n-1, and the honest catch that the sample standard deviation is still slightly biased. 0:00 What is standard deviation? 0:33 How do you calculate standard deviation by hand? 1:59 Why square the deviations instead of using absolute values? 3:04 Why does the sample mean underestimate the spread? 4:34 Why divide by n minus 1? The picture proof 7:34 When should you use n and when n minus 1? 8:54 Is the sample standard deviation unbiased? Sources: https://en.wikipedia.org/wiki/Standar... https://en.wikipedia.org/wiki/Average... https://en.wikipedia.org/wiki/Bessel%... https://mathworld.wolfram.com/Bessels... https://support.microsoft.com/en-us/o... https://www.themathdoctors.org/?p=14709