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How to Use Standard Deviation Formula For Equations (Statistics Help)

Mathmatical Formula for Standard Deviation


Steps to Solving Standard Deviation Problems

Standard Deviation = σ (The Greek letter sigma)

  1. First find the mean of the given set of numbers.
  2. Next subtract the mean from each number in the set.
  3. Then square the sum of each number.
  4. Add the total of the squares together.
  5. Now divide the sum by (n-1).
  6. Then find the square root of your answer for step 5.
  7. You have found the standard deviation (be sure to round accordingly in your given equation).

Example Problem

Find the standard Deviation for the following numbers.

1, 2, 4, 6, 7

First find the Mean of the given numbers.


Now subtract the mean from each numeral.


(2-4)^2 =(-2)^2




Then square the results




2^2= 4


Add all of the squares together


Next take the sum 26 and divide by (n-1).

n is represented by the amount of numbers in the equation which is 5.

Therefore (n-1) equals (5-1) therefore 4.

So 26/4=6.5

Last step is to find the square root of the result which is 6.5.

The Standard Deviation for the given numbers is 2.55 (Rounded to nearest hundredth).

Please Remember

Remember to divide by (n-1) in Step 5. It is a common mistake for students to divide by n.


ashenafi on April 21, 2013:

i have not actual teacher to learn statistics but ihave an interest to learn then i search an other means then got these education and i apprciate u thank u .

khan g on December 14, 2012:

i love stat

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