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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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Why is it so cool to square numbers (in terms of finding the standard deviation)?

I think that is quite obvious. Firstly, the sampling standard deviation measures the dispersion of the data in the samples. You square the difference is to reflect how much the actually data is away …
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