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To paraphrase an old saying: There are lies. There are damn lies. And then there's statistics.

How do you characterize a big heap of data? You could give all kinds of opinions about the information but what would your personal observations mean to people down the street or worse to people half a world away who speak a different language?

Statistics is about counting things. In particular, statistics is a systematic manner of enumerating observations in a repeatable and reportable fashion.

Returning to that heap of numbers we had, one of the measures that is generally used to characterize a set of data is the average. Intuitively we know that what an average is. If we put the data in a dark room and reached in to take a number, we would want to be able to guess how large or small that number might be. We want to know if it was more likely that the number would be two, ten thousand or one trillion. Knowing what the range the number might be in could tell us how to process it. For instance, if we know all the numbers we were likely to get are in the trillion range, we might want to divide each number by a trillion before we began working on it.

Three of the more common means to characterize a data set are the mean, the median and the mode.
Except for specialized data and specialized purposes, the mode is often the most useless of the three. The mode is merely that data point which occurs most often. For instance, in a group of people if the birth date of June 2nd appear the most times, that would be mode. If you are dealing with say a very controlled process with very little tolerance for values other than the mode value, then the mode might be very useful. You could set up an entire process that worked like a charm on the mode value but pretty much rejected everything else. Examples of this might be the nuts, bolts and washers that go on an automobile. You really aren't interested in trying to assemble a car with parts that randomly can be twice as small or twice as large as your target mode value. You might actually want to reject anything that wasn't very, very close to that mode value.

For many of the applications that occur in our world we use the mean or average value to characterize a population. To calculate the average we add up all the values and then divide by the number of values. For groups that have what we call a Gaussian or Normal distribution, this can work quite well. The heights of men or women have a Normal distribution. Normal distributions have

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