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Which mean to use and when? - Cross Validated So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM) Their mathematical formulation is also well known along with their associated stereotypical examples (e g , Harmonic mea
mean - Averaging variances - Cross Validated Context is everything here Are these theoretical variances (moments of distributions), or sample variances? If they are sample variances, what is the relation between the samples? Do they come from the same population? If yes, do you have available the size of each sample? If the samples do not come from the same population, how do you justify averaging over the variances?
What is the significance of 1 SD? - Cross Validated What do you mean by "the derivative at 1 SD is +- 1"? Derivative of what? If you mean of a density plot, then what distribution? The normal? Different distributions will have different derivatives at 1 SD from the mean
What is the difference between mean value and average? The mean you described (the arithmetic mean) is what people typically mean when they say mean and, yes, that is the same as average The only ambiguity that can occur is when someone is using a different type of mean, such as the geometric mean or the harmonic mean, but I think it is implicit from your question that you were talking about the arithmetic mean
Will the mean of a set of means always be the same as the mean obtained . . . The above calculations also demonstrate that there is no general order between the mean of the means and the overall mean In other words, the hypotheses "mean of means is always greater lesser than or equal to overall mean" are also invalid
Mean absolute deviation vs. standard deviation - Cross Validated After calculating the "sum of absolute deviations" or the "square root of the sum of squared deviations", you average them to get the "mean deviation" and the "standard deviation" respectively The mean deviation is rarely used