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I assume "variance of Foo" is linear quantity. Is it true that a variance of 4.0 means "twice as much as 2.0"? If so, then the circle's area (not its radius)
by palish 16y ago
I assume "variance of Foo" is linear quantity.
Is it true that a variance of 4.0 means "twice as much as 2.0"?
If so, then the circle's area (not its radius) must grow proportional to that variance. Growing the radius is an unfair visualization.
The goal is: more pixels = more variance.
- eru 16y agoStandard deviation is the square root of variance. A variance of 4 is twice the variance as one of 2, but that's just by definition. What is perhaps more interesting for your intuition: Adding two independent variables, the variance of the result will be the sum of the variances. Thus the standard deviation of the sum is the squareroot of the sum of squares of the standard deviations of the components. (It's easier to read in formulas.) A look at http://en.wikipedia.org/wiki/Variance http://en.wikipedia.org/wiki/Variance might help.
- palish 16y agoThank you! I really appreciate your explanation. By those definitions, shouldn't the number of pixels (circle area) reflect the deviation, rather than what it currently does (the square deviation, aka variance)? In that case, the area should grow proportionally to the deviation, not to the variance.
- eru 16y agoYou're welcome. I don't know what it should do. Showing variance is fine, and my professor for probability theory actually preferred variance over standard deviation.