Question

As you peruse the internet on statistical concepts, you find that some web-pages show a standard deviation being calculated with n in the denominator and others show a standard deviation calculated with (n − 1) in the denominator (or both!). How does this make sense and when would you use one or the other?

Answer 1

OR

FOR BETTER UNDERSTANDING

When we calculate the standard deviation for a population, we use n in denominator. When we take out a sample from the population and standard deviation is calculated, we use (n-1) as denominator. This is called Bessel's correction.

Bessel's correction is aplied to get 'unbiased' estimator for the population standard deviation. This makes sense because, when we take a sample and calculate the sample mean, we will not get the real population mean, but we get the sample mean. The deviation with respect to the sample mean is calculated here. This deviation will be lesser than the real deviation from the population mean. So, we will get a smaller value for deviation that what it is supposed to be. So, a factor of n/(n-1) is mutiplied (or n-1 is used instead of n) to increase the value of the deviation to what it is actually supposed to be.

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