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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.

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.

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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