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For a set of data $(x_1, \ldots, x_n)$ and its mean $x'$, the standard deviation is calculated by

$$ \sqrt{\frac{\sum_i(x_i - x')^2}{n}} $$ , while the absolute difference of any two numbers can be computed by

$$ \frac{\sum_i|x_i - x_{i+1}|}{n}. $$

What is the difference of those two values?

(Added Below:) Both measure average distance among data points. How do they differ and how are they used in practice?

mallea
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    How they're defined, I guess? I'm not sure what kind of an answer you're looking for. Do you mean their applications, use cases, motivation? If not, what? – PrincessEev Oct 22 '19 at 07:26
  • Sorry for the ambiguity. Both are measuring sort of average distance among data points. In this sense, I'm wondering how they differ and how they are used in applications. – mallea Oct 22 '19 at 07:52
  • Well, all I can say is that the first one is much more popular and used more often. – Matti P. Oct 22 '19 at 07:55

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