Analysis of GIS Data by Simple Examination - Introducing Geographic Information Systems with ArcGIS - page 359

For information to be useful it must have substantial degrees of both precision and accuracy. “How
much” of each? Obviously the issue is complex.

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.

n

∑ 1

x

i n

i 5 1

x 5

i

n

FIGURE 6-8 Formula for average
of a set of numbers

FIGURE 6-9 Sigma: symbol that means
to sum a set of numbers

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 x 1, x 2, x 3, . . . x 12. So when we say xi and i = 7, we are referring to the seventh number, named
x 7. 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 x i . 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,
which is n, or, in this case, 12.

Median

The median number is simply the middle number (or the average of the two middle numbers) in a set of
numbers that has been sorted from smallest to largest (or largest to smallest—it makes no difference). The
median is not sensitive to very large or very small outlying values, as is the mean.

Mode

The mode of a set of numbers is the most frequently occurring number. A set of numbers could have
several modes or none at all.

Range

The range of a set of numbers is the largest number minus the smallest. This gives you an idea of the
spread of the numbers. A better idea of the spread is perhaps the standard deviation, indicated next.