There are two ways of measuring the spread of data. These two ways are known as the mean deviation and the standard deviation.
The mean deviation, or mean absolute deviation is simple. The reason why you con call it mean absolute deviation will be shown later. The first thing you do when calculating the mean deviation is finding the mean of the group of numbers.
Lets make these numbers 1, 2, 3, and 4.
Now, the mean of these numbers is 2.5. The next thing that we do is subtract the mean from the group of numbers.
We end up with -1.5, -0.5, 0.5, and 1.5.
The next thing we do is find the absolute values of the numbers and then find the mean of their absolute values.
So we use the numbers 1.5, 0.5, 0.5, and 1.5. The next step can be written out like this: (1.5+0.5+0.5+1.5)/4= 1
So the mean deviation of the numbers 1, 2, 3, and 4 is 1.
The standard deviation is the more important version of calculating spread, and more complex. In fact, the standard deviation is so important to statistics that it has its own symbol. The symbol is called sigma and look something like this:
This is the Greek lowercase letter for ‘s’, and as mentioned above, is the symbol used for standard deviation.
The first thing were going to do is use the same numbers we used for the mean deviation example. We will use the numbers when they already have had the mean subtracted from them.
In other terms -1.5, -0.5, 0.5, and 1.5. From these numbers, we subtract the mean deviation, 1. We then get the answers -2.5, -1.5, 1.5, 2.5. Next, we square these numbers to get the following: 6.25, 2.25, 2.25, 6.25.
The next step is to find the mean of the squared numbers and the find the square root of the mean. Lets do that.
(6.25+2.25+2.25+6.25)/4= 4.25. The square root of 4.25 is approximately 2.06. So the standard deviation of the numbers 1, 2, 3, and 4 is 2.06.
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