How to Calculate Variance of a Data Set

In statistics, given a sample of elements drawn from a larger population, the variance is a widely-used measure of dispersion. Smaller variances correspond to samples where the elements are clustered closer to the mean, or average, value of the sample. You can compute the variance of a set of elements by performing simple arithmetical operations.

Instructions

    • 1

      Denote the number of elements in the set by "n" and the value of each individual element by "x_i," where i takes values between "1" and "n."

    • 2

      Calculate the sum of all elements in the sample and denote it as "Sum," as in the following formula:

      Sum = x_1 + x_2 + ... + x_n

    • 3

      Calculate the mean of the sample and denote it as "Mean," as in the following formula:

      Mean = Sum / n

    • 4

      Calculate the variance of the sample and denote it as "Variance," as in the following formula:

      Variance = ((x_1 - Mean)^2 + (x_2 - Mean)^2 + ... (x_n - Mean)^2)/n

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