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).
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.
Then square the results
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.
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).
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:
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paxwill on March 12, 2013:
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.
khan g on December 14, 2012:
i love stat