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# Basic Statistics

Statistics may be defined in very erudite ways, but fundamentally, it is the art and science of making a big bunch of numbers into a little bunch of numbers so you can understand stuff about the big bunch of numbers. A GIS can usually do statistics without even breathing hard. Here are some basic statistical measures, most of which you probably know:

## Average

The mean or average: add up all the numbers in a set and divide by the number of numbers. Expressed as a formula the average, called x-bar here, because of the x with the bar over it on the left-hand side, looks as shown in Figure 6-8.

This formula scares some people. It shouldn’t. It simply says what was said in the preceding text. More specifically: Assign integers to each number, like 1to the first number, 2 to the second, and so on until you reach the last number, which we refer to as n. (If there were 12 numbers, n would be 12.) The numbers then are x1, x2, x3, . . . x12. So when we say xi and i = 7, we are referring to the seventh number, named x7. The symbol shown in Figure 6-9 means “take the sum of” whatever follows it. So in the case of the symbol in Figure 6-9, what follows it is xi. What values of i do you use? Those that run from 1 through n, namely, 1, 2, 3, . . . 12. Finally, the formula in Figure 6-8 says divide the sum by the number of numbers, ...

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