The SD quantifies scatter, so clearly you need more than one value! Is two values enough? Many people believe it is not possible to compute a SD from only two values. How many values do you need to compute a SD? But much better would be to show a scatterplot of every score, or a frequency distribution histogram. The only example I can think of where it might make sense to use n (not n-1) in the denominator is in quantifying the variation among exam scores. The goal of science is always to generalize, so the equation with n in the denominator should not be used when analyzing scientific data. The resulting SD is the SD of those particular values, but will most likely underestimate the SD of the population from which those points were drawn. If you simply want to quantify the variation in a particular set of data, and don't plan to extrapolate to make wider conclusions, compute the SD using N in the denominator. The SD computed this way (with N-1 in the denominator) is your best guess for the value of the SD in the overall population. The n-1 equation is used in the common situation where you are analyzing a sample of data and wish to make more general conclusions. But I've seen equations with n, not n-1, in the denominator! Statisticians say there are n-1 degrees of freedom. To make up for this, we divide by n-1 rather than n.īut why n-1? If you knew the sample mean, and all but one of the values, you could calculate what that last value must be. So the value you compute in step 2 will probably be a bit smaller (and can't be larger) than what it would be if you used the true population mean in step 1. Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean. You don't know the true mean of the population all you know is the mean of your sample. Why divide by n-1 rather than N in the third step above? In step 1, you compute the difference between each value and the mean of those values. Take the square root to obtain the Standard Deviation. Compute the square of the difference between each value and the sample mean.ģ.
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