EDIT: okay so i just understood what i’ve calculated is the MAD (mean average distance) of the population. And the use for the standart deviation is that showing how much a set is spread from the mean. The SD is also differentiable and rates outliers higher, please inform me if i got anything wrong.
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For example for a population of (1, 3, 5) the standart deviation is 1.63, what exactly does it represent? Shouldn’t the standart deviation represent how much a data point differs from the mean on average?
Each data point has a 2, 0, 2 difference from the mean, respectively. When we take the arithmetic mean of the 3 differences, we get 1.33, why is the standart deviation 1.63?
I am absolutely fascinated by statistics but sometimes i just don’t get things. I’d be really happy if someone explained this simply, thanks in advance
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In: 0
The standard deviation is the square root of the mean of the _squared_ differences.
In this case your differences are (2, 0, 2), the squares are (4, 0, 4), the mean of that is 8/3, √(8/3) ≈ 1.63
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