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Sample Standard Deviation
So far, we discussed the population standard deviation. Now, let us switch to sample standard deviation(s) that is analogous to the population standard deviation ( σ ). To compute sample standard deviation, the same formula given above has been used replacing μ with and N with n - 1. The modified formula is
s =
s
where,
s = Sample standard deviation
= Sample mean
We use n - 1 as the denominator because unless n - 1 is used, the average of the sample variances of all possible samples (which are obtained by squaring standard deviations) will not be equal to the variance of the population from which the samples have been taken.
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