by Michael Skinner

Created on: May 02, 2009   Last Updated: December 26, 2010

Lies, Damn Lies, Statistics

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

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.

Mode

Three of the more common means to characterize a data set are the mean, the median and the mode.
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.

Mean

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 a bell shaped curve. Most of the data is concentrated in the center of the group so an arithmetic mean is a good characterization of the data.

Median

If you have data that has a lot of variation or data which has many values at the extremes of the data range, then the median might be a better way to characterize the data.

Note that incomes are usually quoted as medians. Medians count the number of objects in a group that have a given value. Then the median is a point at which half the values fall above and half fall below. If we are dealing with a really skewed feudal economy wherein everyone is either very rich or very poor, you might use a median to try to characterize all the data.

Note that with such a skewed data set that the arithmetic average would actually give you the wrong impression of the data. The average would give an income midway between poverty and wealth, but as we stated when we brought up this example, there is no one at this mythical halfway point.

Normal Distribution

One of the characteristics of Normal distributions is that the mean, the median and the mode can all be the same number. In practice what this means is that as humans are Normally distributed, we can make clothes that will fit most people most of the time. If our sizes where as random as say fairy tale creatures then each individual could have such a radically different size and shape than the mass production of every day objects would be impractical.

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