What is the best way to explain the difference between Standard Deviation and Mean Absolute Deviation?

Question

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I’m trying to understand the difference between Standard Deviation and Mean Absolute Deviation (MAD) in reality.

I read somewhere that in SD square makes difference i am thinking that if we square then we also take square-root.

please explain

In: 2

Answer 1

You are correct, the SD is the root of the mean of the squared deviations. Because it’s squared, positive and negative deviations both end up as positive numbers just as the absolute function removes the sign in second one.

But also the squaring the deviations to calculate the SD gives greater weighting to data points further from the mean than a straight average.