# Tag Info

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For any distribution that's roughly normal, you can get a good feel from the 68, 95, 99.7 rule mentioned in the comment. More generally, for arbitrary distributions, the standard deviation measures the variability of the data. More specifically, it measures the average distance of values from the mean. A small standard deviation means that most values are ...

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The comment and @bubba 's answer offer useful technical information. For your use case Let's say for example you are software developer and you need to measure latency of the system over time and present this to the management I'd recommend some care in collecting measurements. The latency is probably highly dependent on system load, perhaps ...

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For general distributions, Chebyshev's inequality is applicable https://en.wikipedia.org/wiki/Chebyshev%27s_inequality. It says that $1-\frac{1}{k^2}$ of the data falls within $k$ standard deviations of the mean. (E.g. $\frac34$ of the data falls within $2$ standards deviations of the mean.)

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The studentized residuals are $$t_i=\frac{\epsilon_i}{\hat\sigma\sqrt{1-h_{ii}}}$$ Where $\epsilon_i$ is the residual, $h_{ii}$ the leverage and $\hat\sigma$ is the estimate of the standard deviation of residuals, that is $$\hat\sigma^2=\frac1{n-m}\sum_{i=1}^n\epsilon_i^2$$ Where $n$ is the number of observations (here $4$) and $m$ the number of ...

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If we sample from $X\sim N(150, 40^2)$ 100 times, then the sample mean is $$\bar X = \frac{X_1+\dotsb+X_{100}}{100}.$$ Then \begin{align*} \text{Var}(\bar X) &= \text{Var}\left(\frac{X_1+\dotsb+X_{100}}{100}\right) \\ &=\frac{1}{100^2}\text{Var}(X_1+\dotsb+X_{100})\\ &= \frac{1}{100^2}\cdot100\cdot\text{Var}(X_1) \\ &= \frac{40^2}{100} ...

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