> mean versus medians, confidence levels or margins of error

It's basic when you are attending an undergraduate course but most people can understand mean (as a dictionary might generically define it) and have a general feeling for margin of error (again, not in the mathematical way.)

Statistics has been the most difficult course in my CS course. For some reason when I start counting events to get a probability I find several perfectly plausible ways to count them, get five different probabilities and none of them is the correct answer.

And about being "trivial to manipulate [numbers] to generate the headline you want" a politician once told me that you can show the same numbers in any way you want, as in to demonstrate a thesis or its opposite.

With large sets or sequences of numbers approaching almost infinity, counting as a method of determining how large things are ... doesn't work well as you found out. To determine if ginormous set A is larger than ginormous set B, you have to do things like matching-pairing. For every element in set A, pair it with an element of set B; if you exhaust all of the elements in B but still have elements in A... then set A is larger than set B.

To formulate the probability of B happening, for example, you have to make an educated guess. Create a functional equation that map A (all possibilities) to B (desired possibility). Then you make a ratio-fraction with the equation in the numerator and set A in the denominator. Using Algebra, try to eliminate references to A in both the numerator and denominator to give you an educated guess of what the probability is.

In college, studying mathematics, probability was the course in did best in. The funny part is that I have a form of ilnumeria. Effectively I can’t count. As a result I have no desire to try to actually count things, and the easiest way for me to cope is by understanding the theory behind counting.