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How to Calculate Standard Deviation

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How to Calculate Standard Deviation

1,335,020 views October 25, 2010 1:29

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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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Howcast published this 1:29 video tutorial on October 25, 2010. It has been watched 1,335,020 times on YouTube.

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Howcast
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October 25, 2010
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Further reading

  • Standard deviation: calculating step by step (article) | Khan ... khanacademy.org

    Calculating standard deviation step by step. This is the currently selected item. Practice: Standard deviation of a population. Mean and standard deviation versus ...

  • Standard Deviation Formulas - MATH mathsisfun.com

    Standard Deviation Formulas. Deviation just means how far from the normal. Standard Deviation. The Standard Deviation is a measure of how spread out numbers are. You might like to read this simpler page on Standard Devi…

  • How to Calculate Standard Deviation: 12 Steps (with Pictures) wikihow.com

    To calculate standard deviation, start by calculating the mean, or average, of your data set. Then, subtract the mean from all of the numbers in your data set, and square each of the differences. Next, add all the squar…

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