The basic standard deviation equation is:
SEE IT'S CONFUSING.
If this was your first reaction too, it's okay. It's much easier when you break it down, I promise!
I find it's easier if you think about the concepts of the equation (i.e. WHAT does this equation tell us to do?)
Step 1: To find standard deviation you start by finding the average of your set of numbers. I'm sure most people know how to find the average, but it's found by adding up all of the numbers and then dividing that sum by how many numbers there are.
After you've found the average, you can start using the equation.
Step 2: To find SD (that's standard deviation, I like to abrev), you take each individual number in your set of data and subtract it from the mean. Then you square that number. You do this for each number in your set of data and add them together.
Ex: If your average is 10, and your data contains: 15, 12, 14, 11
(10-15)^2 + (10-12)^2 + (10-14)^2 + (10-11)^2
Step 3: Next, you divide the number you found in Step 2, by how many numbers there are and subtract one.
Ex: Using our example from above. There are four numbers so we would divide by (4-1).
Step 4: Once you have your number you need to find the square root of that and then, you've found the standard deviation!
But what did you actually just find?
Well, the standard deviation shows you how much the data deviates away from the mean.
- 68% of the data lies within one standard deviation of the mean.
- 95% of the data lies within two standard deviations of the mean.
- 99.7% of the data lies within three standard deviations of the mean.
Once you understand the equation for standard deviation and what all the symbols mean, you can find out a lot of information from looking at a bell curve like the one above. Understanding standard deviation is a great asset because it allows you to interpret data, and bell curves are a type of graph you will encounter throughout your life, especially as educators!
