“Some questions are more easily asked than answered” Edward Sapir(?)

Possibly the most frequently asked and least frequently answered question is why does the definition of the standard deviation involve division by n-1, when n might seem the obvious choice. This is a question which perplexes introductory statistics students and calculator manufacturers alike. The explanations given in calculator manuals tend to range from obscure to fanciful, and both options are given on the keypad, usually labelled s_n-1 and s_n to add to the confusion. (The symbol s is reserved for the standard deviation of a random variable or a population/distribution, an entity which lecturers valiantly try but usually fail to keep distinct from its sample counterpart.) Australian students first meet the standard deviation in secondary school, where the definition given does indeed involve division by n. This definition is preferred to avoid the question about the n-1 being raised it would seem. Secondary school teachers have a hard enough life as it is. And it must be remembered that the difference between the two definitions is largely academic for all but the smallest of sample sizes (say, less than 10 observations). So, don’t get too agitated by the revamped definition. The truth can be told but the telling usually quells the desire to know. If the fire still burns in your belly, read on.
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