Sample Variance: Definition, Formula & Example

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

Do you understand the difference between sample variance and population variance? This lesson will explain when to use sample variance and give an example calculation.

When to Use Sample Variance

Nell has just landed a job at a large insurance company. Her boss, Levi, is explaining one of her first job assignments.

'I need you to calculate the variance for this medical procedure. We already know that the mean is $111, but the variance is also useful to us when we are setting how much we will reimburse hospitals. I'll send you the data file by email. Let me know if you have any questions.'

When Nell later gets the files, she finds that there are thousands of individual data points for this procedure. The formula she knows for variance requires using all of these points. Just entering them would take her days! She writes back asking for clarification.

Definition and Formula for Sample Variance

Levi responds, 'The formula you are trying to use there is population variance. What I want you to do is to use a few of the data points--say, 15--to estimate the variance of the entire population. This is called sample variance.'

Now she gets it. Sample variance is how much the measurements in a sample differ from each other. Things are much clearer for Nell, who promptly looks up the formula for sample variance:

Sample Variance

Note the sigma character above---the odd-looking E summation symbol---means that you add up everything that follows it in the set.

Example

Now that Nell has the correct formula, she creates a spreadsheet with three columns, enters some of the data points for the first column, and uses the formula to fill in the other columns. She comes up with something that looks like this:

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