Standard Deviation Formula

 standard deviation formula that you will use to find the standard deviation is shown below.

Standard deviation formula


x represents a set of numbers. For example, x could be 5, 6, 14, 1, 6, 10

mean is the average of the set of numbers

Σ means sum or addition

n is the size of the list. For example, for the set above, 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.

Σ(x - mean)2 / n


Step 5: Take the square root of the average found in step 4


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


mean =
25 / 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

-12 = 1
12 = 1
32 = 9
-32 = 9
02 = 0

Step 4: Add 1, 1 9, 9, and 0. Then divide by 5

1 + 1 + 9 + 9 + 0 / 5


20 / 5
= 4


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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