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# How to Calculate Standard Deviation

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.

### Instructions

- 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. - FACT: The term "standard deviation" was first used by statistician Karl Pearson in 1893.

### You Will Need

- Data
- A calculator