Bayesian methods

The problem with tracking tiny probabilities like 0.0001%, aside from the rather larger chance of human error, is that no-one can feel a probability that small. If you must talk about such numbers anyway, remember: though you can write a symbolic description of this probability, a feeling that small doesn't exist, doesn't fire enough neurons or release enough neurotransmitters, so it's not actually an object worth keeping track of consciously (you'd lend it overmuch respect), any more than any Flying Spaghetti Monster proposition.

So when the math gives you a number this small, discount the hypothesis entirely. The only cause for doubt is the question of whether you did the math correctly. The thought "ok it's tiny, but not zero, so there's still a chance, right?" is one you should be wary to ever find yourself generating.

Plus if you Visualize probability as shades of grey, the human-perceptual difference between the black of 0.0001% and the black of 0% is… indistinguishable. Why then keep any track of 0.0001%?

Shades of grey. There are shades so bright as to be essentially white, and shades so dark that for all intents and purposes, they're black.

arithmetic mean:

x1 + x2 + x3 __ 3

geometric mean

x1 * x2 * x3 __ 3

Used when the involved quantities have different scales.

Mean, median, mode (modal means 'typical').

Usually it's the median or the mode that's more informative than the mean. To be intellectually honest (maybe related: Responsible Research), journalists could just adopt the practice of reporting all three, or at least never using the word "average" in favour of specifying mean, median or mode. Even better, show the shape of the distribution anytime an average is mentioned, so we're reassured it's not multimodal or something else weird. Actually upon reflection, I find it odd and disturbing that it isn't already the norm in newspapers & blog articles to show the distribution.

Q: Can mode be calculated for continuous data? How? Interpolate a kernel density curve and find its tallest peak?