Answer

If you follow that procedure for calculating the standard deviation, you will get zero every time. Roughly, this is because the mean is in the middle of the data set, so subtracting the mean from each number in the data set will give negative numbers as well as positive numbers. If you're interested, here's the proof. If the data set consists of the numbers $x_1, x_2, \ldots x_N$ , then the mean $\bar{x}$ is given by $\bar{x} = (x_1 + x_2 + \ldots + x_N)/N$ . If we subtract $\bar{x}$ from each number in the data set, and then take the mean of the resulting numbers, we get

$\begin{eqnarray*} \mbox{Mean} & = & [(x_1 - \bar{x}) + (x_2 - \bar{x}) + \ldots ... ... + x_N)/N - N\bar{x}/N \\ & = & \bar{x} - \bar{x} \\ & = & 0 \end{eqnarray*}$

The actual method for calculating the standard deviation uses the square of the distance from each data point to the mean. Since the square of a number is always positive, this problem is avoided.

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