# Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate]

$$Mean\;Absolute\;Deviation = \frac{1}{n}\sum_{i=1}^n |x_i-mean(X)|$$ Almost all textbooks and papers are using Standard Deviation as a measurement of dispersion. And of course, almost all the models are built based on Standard Deviation.

But I don't understand how Standard Deviation has gained such popularity. I mean, Mean Absolute Deviation is a very intuitive measurement of dispersion. It tells you exact average distant that each value deviates from their mean. Standard Deviation, on the other hand, makes the result more sensitive to outliers. Why we need this sensitivity. Is there any historical reason leads us to use SD way more often than MAD?

• Something something absolute function not differentiable. – user2974951 Oct 10 '18 at 8:11
• Both are used in empirical research. Standard deviation is more convenient mathematically, probably among other reasons. – Xiaomi Oct 10 '18 at 8:23
• A few potential reasons: it's differentiable, the Normal Distribution naturally parammetrises in terms of its standard deviation, the true mean minimises the expected variance (whereas the true median minimises the expected MAD) – gazza89 Oct 10 '18 at 8:43
• I am voting to close this question because it has been asked several times before. However, it is useful and it could serve some purpose as helping in searches. For instance I seem not to find the post that I had in mind when marking this as duplicate (although several other posts came up that are obvious duplicates as well). – Sextus Empiricus Oct 10 '18 at 11:03
• stats.stackexchange.com/search?q=gorard it will relate to the 118th question on this website – Sextus Empiricus Oct 10 '18 at 11:13