Month: July 2025

Formulas for Standard Deviation: More Than Just One!

Last time we introduced standard deviation. Here we’ll look into why two formulas (namely, population and sample standard deviation) are different, and why several different formulas for either are equivalent. We’ll also discover how to update the standard deviation when a new value is added. In doing so, we’ll see some different perspectives than we …

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Standard Deviation and Its Rivals

We’ve had a number of questions about “measures of dispersion”, such as standard deviation, which tell us how much data spreads out, as opposed to “measures of central tendency”, which tell us where the middle of the data is (as we discussed in Three Kinds of “Average” and Mean, Median, Mode: Which is Best?). Why …

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Arranging Letters in Words, Revisited

A recent question illustrates well the different ways to solve problems in combinatorics. We’ll see an easy way, another easy way, and a … less suitable … way to solve a set of problems.

Is There More Than One Standard Form for an Equation?

A couple recent questions asked what constitutes “standard form” for a quadratic equation; that will lead us to some older questions about “standard form” for a linear equation. We’ll see that “standard” isn’t quite as standard as you might think.