How Do You Calculate Statistical Sample Variance?

# How Do You Calculate Statistical Sample Variance?

To calculate the sample variance of a population, first determine the mean of the sample, subtract each data point from the mean, square each resulting number, add all the squared results together, and then divide that number by the total number of points in the data set minus one. A one is subtracted from the total number of data set points in the dividend to compensate for not considering the whole population.

To find the mean of a data set, add up all the numbers together, and divide the result by the number of points in the data set. For example, the mean of 6, 11 and 8 is 8. After subtracting each data point from the mean, the numbers are squared to eliminate any possible negatives. In the previous example, subtracting each data point from the mean and squaring the number results in 4 + 4 + 0 for a total of 13. This number is then divided by the number of data points in the sample minus one, or in this example, two. The sample variance is therefore 6.5.

Sample variance shows the spread of a set of data points. A sample variance varies from a population variance in that it calculates variance using data from only part of the population instead of all of it. However, sample variance is used to characterize the entire population.

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