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If you want to find out the uncertainty or standard error (SE) in the standard deviation of a chosen sample, then you can simply use $SE(\sigma) = \frac{\sigma}{\sqrt{2N - 2}}$, where $N$ is the number of data points in your sample. Hope that helps!


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If you're allowed to take that sample repeatedly, it's basically bootstrapping. Procedure: Draw 100 points Calculate standard deviation Repeat Steps 1 & 2 a lot of times (empirically, I've found 5-10,000 to be enough), keeping track of the results of step 2. Examine the distribution of estimates from Step 2 with whatever tools you'd like -- ...


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You're probably familiar with the interpretation of the $z$ score as "the number of standard deviations the test statistic is from the mean". This interpretation can be obtained from the formula for the $z$ score. Consider, $$z = \frac{x-\mu}{\sigma},$$ if we multiply $\sigma$ to the left hand side we get, $$ z \sigma = x-\mu,$$ here we see that ...


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The sample coefficient of variation is the sample standard deviation divided by the sample mean. Here is an illustration: Which has greater variability, weights of elephants or weights of ants. In terms of the standard deviation the answer has to be elephants because they weigh more. Dividing by the mean tends to put the two measures of variability on the ...



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