MAD & Standard Deviation

[Agent Smith]

How closely do they track each other?

$\displaystyle \text{MAD} = \frac{1}{n} \sum_{i = 1} ^ n |x_i - \mu|$

$\displaystyle \sigma = \sqrt{\frac{1}{n} \sum_{i = 1} ^n \left(x_i - \mu \right)^2}$

 

[Dr.Peterson]

How closely do they track each other?

$\displaystyle \text{MAD} = \frac{1}{n} \sum_{i = 1} ^ n |x_i - \mu|$

$\displaystyle \sigma = \sqrt{\frac{1}{n} \sum_{i = 1} ^n \left(x_i - \mu \right)^2}$

Have you tried looking it up?

Average absolute deviation - Wikipedia

en.wikipedia.org

Mean Absolute Deviation: Definition, Finding & Formula

The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between each observation and the mean.

statisticsbyjim.com

Quick answer: they are different numbers, not at all the same, and they behave differently (e.g. in the effect of outliers).