# How to Calculate the Variance for Grouped Distributions

by Owen Pearson

A grouped distribution can provide valuable information about the performance of individual investments in your portfolio, as well as the overall performance of your investments. The variance, or the difference between values of a distribution and the mean of the group distribution, can show you the extent to which a particular investment underperforms or overperforms. Simple calculations can help you determine the variance of the values of a grouped distribution.

1. Add each value in your grouped distribution with a calculator. Divide the sum by the total number of values in the distribution. This gives you the mean value of the grouped distribution. For example, if you have three investments with 3-percent, 5-percent and 6-percent earnings, add the earnings values to obtain a total of 14. Divide 14 by 3 to obtain a mean of about 4.67.

2. Subtract the mean from each value, and then square the result of subtracting the mean from each value. For example, subtracting 4.67 from 7 gives you 2.33. Square 2.33 to get about 5.249.

3. Add the squared values together. Divide the sum of the squared values by the number of values in the grouped distribution. For example, if the total of the squared values equals 8.468, and you have three values, divide 8.468 by 3 to obtain about 2.829. This number represents the variance of the grouped distribution.

#### Warning

• Avoid using variance as the sole means of evaluating an investment. Other factors, such as economic changes and investment goals should influence your investment decisions.

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