Standard Deviation Formula
The standard deviation formula that you will use to find the standard deviation is shown below.
As you can see, x represents a set of numbers. For example, x could be {5, 6, 14, 1, 6, 10}.
The mean is the average of the set of numbers.
The symbol Σ refers to an addition.
n is the size of the list or set. For example, for the set above or {5, 6, 14, 1, 6, 10}, n = 6.
σ is the symbol used for standard deviation.
Steps to follow when calculating the standard deviation
Step 1: Find the mean of the set of data (mean).
Step 2: Find the difference between each value and the mean (x  mean).
Step 3: Square each difference or each answer you got in step 2 (x  mean)
^{2}.
Step 4: Add all the answers you got in step 3 and then divide by the number of answers to get the average.
Step 5: Take the square root of the average found in step 4.
A good example that shows how to use the standard deviation formula to find the standard deviation.
Using the standard deviation formula, I will now show you how to get the standard deviation step by step.
Let S = {4, 6, 8, 2, 5}
Step 1: Find the mean of S = {4, 6, 8, 2, 5}
mean =
4 + 6 + 8 + 2 + 5
/
5
Step 2: Find the difference between each value in S = {4, 6, 8, 2, 5} and 5
4  5 = 1
6  5 = 1
8  5 = 3
2  5 = 3
5  5 = 0
Step 3: Square each difference or each answer you got in step 2
1
^{2} = 1
1
^{2} = 1
3
^{2} = 9
3
^{2} = 9
0
^{2} = 0
Step 4: Add 1, 1 9, 9, and 0. Then divide by 5
Step 5: Take the square root of the average found in step 4. That is the standard deviation
Standard deviation = σ =
√4
= 2

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