Instead of memorizing the formula, I tried to understand the concept of standard deviation at the most fundamental level I could visualize. For instance, standard deviation is a measure of the amount of variation or dispersion of a set of values. Let's say I want to measure the variance of the distance (let's ignore the direction) I travel on a daily basis in a given month. I would sum the squared differences between daily distance and the average distance. In my head, I visualize a theoretical area, composed of many squares with each side equal (x-u). Hence, big outliers like a road trip would greatly affect the outcome.

 

What if I substitute money in place of distance? Could I use something other than the mean as the 'benchmark'? Could I use a fixed value (e.g. budget) or other fundamental or technical values like moving averages? Or how about I scale the differences based on some criteria (e.g. differences get inflated if they cross a threshold) Or could I time-weigh the differences (e.g. use a scaling factor to place more weight on recent data)? Would any of these alternatives more accurately measure risk? How about using the concept of standard deviation in places like handwriting recognition (e.g. what's the "total area" of errors)? Understanding the fundamental principles of any knowledge, I believe, makes that knowledge more "pluripotent"; thereby giving it power to proliferate in an unpredictable manner.

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