1) "Variance in number of comments" is visualized as a circle's radius.
2) ... But a circle's area increases as (pi)r^2. That's an exponential increase.
A fair visualization would show a linear increase, not an exponential one.
EDIT: To be more clear, the goal is "more pixels" = "more variance". Growing the visualization by a radius is inherently unfair.
It's precisely these kind of subtleties that make statistics such a fallacy minefield.
No, no, no, no, no. "exponential" != "has an exponent". Exponential means the variable is the exponent, as in 2^n. The word you're looking for is "quadratic".
Or are you trying to educate me out of good will? If so, thanks.
Oh, it's an exponential increase in 2, but a linear increase in Pi.
Anyway, just pretend that the area of the circle is proportional to the variance, and the radius to the standard deviation.
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.
A look at http://en.wikipedia.org/wiki/Variance might help.
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.
I don't know what it should do. Showing variance is fine, and my professor for probability theory actually preferred variance over standard deviation.