Let $\{x_{i,j} : i=1..7,j=1,..n\}$ be a set of samples from $n$ weeks (where $i$ denotes the day of the week). Is there any interesting information to be gleaned from the relationship (ratio, difference, etc.) between $ \mathbb{E}_{i} [std(x_i)]$ and $std(x)$?
Relation of mean of standard deviations and standard deviation
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statistics
standard-deviation