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






New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Follow me on Pinterest


Page copy protected against web site content infringement by Copyscape

Recent Articles

  1. Number Game

    Dec 01, 16 06:27 AM

    1. Think of any positive whole number. No fractions, no decimals,no percents. 2. Double that number. 3. Add 10 to that result in step 2. 4. Divide

    Read More