Well I think it's bloody awesome that you want to understand standard deviations rather than to just calculate them by shoving the numbers into a calculator (or worse, Microsoft Excel
). Standard deviation is a measure of the spread of data. You can have a bunch of numbers that are all really close to each other, for example:
There are 11 numbers here
Step #1: work out the Mean
. This is done by adding the value of all the numbers and dividing that by the number of numbers (i.e. 11). So (1+2+3+4+5+6+6+6+7+7+8) divided by 11.
Step #2: from each of the above numbers, subtract the mean (so take away 5 in this case, and it's totally cool to get minus numbers here).
.. here's what you get
-4, -3, -2, -1, 0, 1, 1, 1, 2, 2, 3
Step #3: square each number and you get...
16, 9, 4, 1, 0, 1, 1, 1, 4, 4, 9
Step #4: add all these numbers up and you get...
Step #5: divide this number by the number of numbers (which as we know is 11) MINUS 1. So divide by 10 in this case, and we get ...
Step #6: get the square root of the resulting number. So the standard deviation here is 2.24
Aint that cool
? Try working out the standard deviation now for a whole load of other numbers, so you can understand it better. The bigger the spread in the data, the bigger the value for standard deviation. Why? Because the bigger the spread, the more different the numbers will be from the mean. So you'll get much bigger numbers in step 2. The numbers in step 2 then get squared and added together, so go figure ^^