## Distributions

A while back read a discussion about what increase in pay is worth changing jobs. Whether or not you change jobs for an extra 100 $currency depends on how much you are making: we tend to make that decision on a percentage (thus, higher incomes requires higher increases to be appealing). In other words, we tend to want to multiply our income, not add a certain fixed amount with each successive job.

In another article which I can’t remember, it was stated that incomes (and rents) are distributed as a log-normal distribution, rather than, what apparently is intuitive to many, a normal distribution. It explains why looking at the **mean** income is misleading, the mean is really only for normal distributions a good measure of central tendency.

In my first article it took me a while, whilst studying uncertainties in scoring quantities per voxel, to realize that a mean uncertainty didn’t make sense. After a long time, I figured out that with a logarithmic x-axis, I suddenly got my bell curve back. Since then, I am weary when papers report their mean uncertainties, and leave out their medians.

Thanks to ol' hn, now I know why. Although I had learned before that when you add independent quantities, you get the famous bell curve, the Gaussian. It has a nice name, the Central Limit Theorem. I never thought much of it, until I read this very succinct post: Why isn’t everything normally distributed?. Quote:

Incidentally, if effects are independent but multiplicative rather than additive, the result may be approximately log-normal rather than normal.

Aha! So by knowing the distribution, we know something about the nature of the observable. Interesting! I really missed a good statistics education, but slowly I am piecing together very useful knowledge!