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Why is it important to divide by df to compute sample variance?

Why is it important to divide by df to compute sample variance?

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Answer #1

So to answer this question, lets look at the formula for sample variance:

The sample variance is:

It is the sum of square of deviations from the mean. So if we do not divide by the variability we would be getting the total variability in the data. We do not want that. We want the average of the sum of deviations from the mean, which would provide us with a better idea about the spread by which the values vary in order to draw valid statistical conclusions. Thus it is pivotal to divide by the degree of freedom.

Please let me know in comments if anything is not clear. Will reply ASAP. Please do upvote if satisfied!!

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