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How to Calculate Standard Deviation

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Published on Mar 23, 2010

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Standard deviation quantifies how diverse the values of your data set are, and is useful in determining how different your numbers are from each other.

Step 1: Collect your data
Collect your data to create the data set from which you wish to calculate the standard deviation.

Step 2: Calculate the mean of the data set
Calculate the average, or mean, of the data set by adding all of the numbers of the set and dividing the total by the number of items in your set.

Tip
Calculate the mean of a set consisting of two, five, six, and seven by adding two plus five plus six plus seven, and then dividing by four – the number of items in your set. The mean is five.

Step 3: Subtract the mean from each number; square result
Subtract the mean from the first number in your data set, and square the differences. Continue with each number in your data set.

Tip
With the set consisting of two, five, six, and seven, calculate two minus five and get negative three. Square that for a total of nine. Continue with the other numbers in the set.

Step 4: Add squares together; divide by number of items
Find the mean of the differences. Add the squared differences and then divide the total by the number of items in data in your set.

Step 5: Take the square root to find standard deviation
Take the square root of this mean of differences to find the standard deviation.

Did You Know?
The term "standard deviation" was first used by statistician Karl Pearson in 1893.

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