So I learned that standard deviation is as such that if there is a set:
with the average:
Then the standard deviation is:
But a while ago, I was told that this works too (and I checked it, and it seems to work):
If given the set:
with the average
and the average of the square of each :
then the standard deviation is as follows:
Why is it that the second way of getting standard deviation right? In other words, how do I derive the second way from the first way? The main reason I am having trouble figuring this out is that it seems to make the assumption that:
Which if I recall correctly, is not true because: