How to Find Standard Deviation:
4 Simple Steps
Here we explain how to find standard deviation. You should know the terms mean and variance before hand. But if not, there are links below for more details.
1. Find the mean
The first thing you will need is the mean of your set of numbers. Here’s a calculator if you need one Mean Calculator. If you are unsure of how to find the mean, here is an explanation How to Find Mean: 3 simple steps.
2. Calculate (x – mean)2 for each x value in your set and square it.
Subtract the mean from each x value and square the result. After squaring, the result should always positive.
3. Find the average of the step 2 numbers
Find the average of the all the ‘squared differences’ from step 2. Since mean is the average, you can use the mean explanations from step 1. But this average is called the Variance.
4. Take the square root of step 3 result (Variance).
Take the square root of the variance. If you already know the variance, finding the standard deviation is as simple taking the square root of the variance.
Example: 8 students each take a test. The test scores are 67, 72, 74, 79, 79, 81, 84, 94. Find the standard deviation of the test scores.
1. Find your mean
mean = 78.75
2. Calculate (x – mean)2 for each x
The last column in Figure 1 below is the list of results
3. Find the average
138.06 + 45.56 + 22.56 + .06 + .06 + 5.06 + 27.56 + 232.56 = 471.5
471.5 / 8 = 58.94
4. Take the square root
sqrt( 58.94 ) = 7.68
So the standard deviation = 7.68
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Would you like us to find the standard deviation for you? Use my latest calculator! Calculator: Stat summary
My explanation leave you needing a little more? These guys do a pretty good job. Khan Academy – Standard Deviation
Thanks for reading!