# 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)

- First find the mean of the given set of numbers.
- Next subtract the mean from each number in the set.
- Then square the sum of each number.
- Add the total of the squares together.
- Now divide the sum by (
*n*-1). - Then find the square root of your answer for step 5.
- 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.**

## Comments

i love stat

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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