Thanks very much. Where did the 68, 95, and 99.5 percentages come from? It all seems rather arbitrary.
Hi again, Le Chef. Again, in simple language, the equation which describes the bell curve and the data we can get from it, such as the percent of instances which fall within [and outside of] a number of sd's, isn't arbitrary. Think of a simple pachinko pinboard. If we drop ball after ball from the top center of the board, they'll pile up into a bell curve. That curve can then be described mathematically by finding an equation which 'fits' the curve. Once we have the equation, it's 'Nelly, bar the door!' We can use the equation to come up with all sorts of things about that pile-up of individual pieces of data. The percent numbers I stated came from measuring the actual areas under the bell curve that include specific sd limits. They're rounded off. Standard deviation is itself the product of an equation. We get it by taking all of the numbers in our sample, entering them into the equation and turning the mathematical crank, so to speak. Out pops a single number - the standard deviation. How accurate it is depends upon the sample size, the accuracy of the measurements and how well the data, if we had lots and lots of it, fit the bell curve equation. To sum up, we can get the bell curve equation from a controlled 'experiment' such as the pachinko pinboard or a mathematical equivalent. Then we can see how well 'real life' piles of numbers such as the decisions of judges in certain types of cases fit the 'curve'. If we find a good fit, we can use the equation to make excellent guesses of many kinds about that type of number/data. Nice chatting with you. Your questions are very sensible.
