Anonymous
Post 11/15/2024 13:45     Subject: Why is the square root of the average squared distance from the mean more important than…

The first definition is variance, or standard deviation squared, and a useful statistic when dealing with a large number of samples from a uniform distribution. It allows you to make predictions about the samples.
Anonymous
Post 11/14/2024 15:52     Subject: Why is the square root of the average squared distance from the mean more important than…

They both have utility, but the former is preferred because it’s actually simpler when you are doing a line of best fit. (Doing the calculus with absolute values is messy). It’s also more sensitive to outliers, which is often what people want.
(The average of 2,3, and 10 is 5, the root squared average is 5.3. The average of 2,3,100 is 35. The root squared average is 58.)
Anonymous
Post 11/14/2024 08:34     Subject: Why is the square root of the average squared distance from the mean more important than…

There is a right triangle and Pythagoras somewhere in the reason
Anonymous
Post 11/13/2024 20:56     Subject: Why is the square root of the average squared distance from the mean more important than…

the average absolute distance from the mean?

The latter seems much more straightforward.