There is nothing wrong with STD or MAD. The real problem is a lot of people apply them without realizing the nature of their data and what kind of analysis they

There is nothing wrong with STD or MAD. The real problem is a lot of people apply them without realizing the nature of their data and what kind of analysis they want to do. In this case what matters in the end is the kind of impact deviation from mean has on the real world variable you have. I agree that in most Gaussian experiments MAD might be more useful than STD. STD is more useful when the real world impact of the deviation increases exponentially with the magnitude of deviation and hence it is a good idea of magnify the (x-n) by squaring it. In many cases the impact is linear where MAD clearly works better. For example in cricket where n runs are n times better than 1 run. But in case of shooting. Hitting 9 targets out of 10 might be 100 times better than 1 out of 10 so there MAD will be misleading.