Why do we need to know the deviations from the mean to compute the variance?
What is the logic behind this? Why not use any other data point like the median or mode or anything else? What if the mean is already skewed as it’s pulled by an extreme outlier?
When it comes to the general spread, even beyond the variance, why use the mean when the mean itself is unreliable with outliers?
As in the calculus derivations behind everything in statistics? Does anyone love exploring the math engine behind the formulas?
Does anyone try to break the formulas and add their own flavor to see what happens?
Does anyone question what happens if we stop taking the square root of a variance, for example, and start using absolute values for fun?
Is this a valid hobby or a sign you are an outcast?
As in the calculus derivations behind everything in statistics? Does anyone love exploring the math engine behind the formulas?
Does anyone try to break the formulas and add their own flavor to see what happens?
Does anyone question what happens if we stop taking the square root of a variance, for example, and start using absolute values for fun?
Is this a valid hobby or a sign you are an outcast?
My problems with proof writing are:
my proofs sometimes become invalid due to a missed edge case
my proofs’ logic is so far from the correct answer despite rigorous checking from my side
my proofs sometimes state the obvious when I was supposed to prove it. I handwaved the logic and didn’t explain why it was true
I’m not sure what to do even with 2). I don’t know how to fix my logic because I believe it’s correct only to see it’s far from the right answer