How to Find The Sample Variance and Standard Deviation

By Bethany Smith
Knowing how to calculate percentages can be useful.
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Variance and standard deviation are statistical tests that can be performed to explain the data found in a certain sample. A sample is a set of numerical data. It usually includes results from a survey or experiment. Variance of the sample measures how far the results are from the expected results. Standard deviation expresses how close the results are to each other. Together, these tests give information about the range of the results.

Find the mean of the sample. The mean is the average of all of the results in a sample.

Subtract the mean from the first value in the sample. Square this value.

Repeat Step 2 for each number in the sample.

Add each of the values found in Steps 2 and 3 together.

Find the total number of results in the sample, minus one.

Divide the value found in Step 4 by the value found in Step 5. This is the sample's variance.

Find standard deviation by taking the square root of the value found in Step 6.

About the Author

Bethany Smith has been writing since 2004. Her articles have appeared in the “Charlotte Sun Newspaper” and “Harbor Style” magazine. Smith interned at her local newspaper in high school and has worked as a freelance writer throughout college. Smith will graduate from the University of Florida in 2011.