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The variance is based on the squares of the variable being studied. If, for example, the variable is mass, then the variance is measured in mass-squared. Most people will not be able to wrap their heads around the square of mass. However, the square root will be in the same units of measurement as the variable itself. Thus, the idea of a variable being distributed about a mean, M (also measured in the same units), with a standard deviation (or error) of S is easier to understand.

Second, under reasonable conditions,the transformed variable obtained by subtracting the mean and dividing the result by the standard deviation will have a standard normal distribution. This is extremely important for estimation and hypothesis testing.

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Q: Why take the square root of the variance when calculation standard deviation?
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