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

Updated on August 12, 2013

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.

20/5=4

Now subtract the mean from each numeral.

(1-4)^2=(-3)^2

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

(4-4)^2=(0)^2

(6-4)^2=(2)^2

(7-4)^2=(3)^2

Then square the results

-3^2=9

-2^2=4

0^2=0

2^2= 4

3^2=9

Add all of the squares together

9+4+0+4+9=26

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.

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      ashenafi 4 years ago

      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 .

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      paxwill 4 years ago

      Actually, it is correct to divide by n if the data represents the entire set being studied. You only divide by n-1 when your set is a sample taken from a larger set. The first case is called the population standard deviation, the second is called the sample standard deviation.

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      khan g 4 years ago

      i love stat