How to Calculate the Variance of a Gaussian Curve

The Gaussian Curve is more commonly known as the Bell Curve. It forms a hill or "bell" shape wherein the 66 percent of a population sample falls with one standard deviation of the midpoint and 95 percent of the population falls within two standard deviations. The variance for the Gaussian Curve is one important component and is represented as sigma squared (σ^2).

Instructions

    • 1

      Compute the average of the set of the numbers in the curve. You will need the data set of the curve for this number. Simply sum all of the numbers and take the average of them. For example, if the numbers are 0.5, 3.3, 4.5, 5.0, 5.5, 6.6 and 9.5 then the average is 4.9.

    • 2

      Find the deviation from the mean for each number. That means that you subtract the average from each individual number. If the average 49 is taken from each of the numbers the results are as follows:

      0.5 - 4.9 = -4.4

      3.3 - 4.9 = -1.6

      4.5 - 4.9 = -0.4

      5.0 - 4.9 = 0.1

      5.5 - 4.9 = 0.6

      6.6 - 4.9= 1.7

      95 - 49 = 4.6

    • 3

      Square the difference of each of these numbers next. The result would be the following:

      4.6 Squared = 21.2

      1.7 Squared = 2.3

      0.6 Squared = 0.4

      0.1 Squared = 0.01

      -0.4 Squared = 0.2

      -1.7 Squared = 2.9

      -4.4 Squared = 19.4

    • 4

      Add up all the squares and then divide by the number of points to find the average, this is the variance.

      (21.2 + 2.3 + 0.4 + 0.01 + 0.2 + 2.9 +19.4)/6 = 7.4

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