How to Calculate Relative Standard Error

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    • 1). Compute the mean of the sample by dividing the sum of the sample values by the number of samples. For example, if our data consists of three values--8, 4 and 3--then the sum is 15 and the mean is 15/3 or 5.

    • 2). Compute the deviations from the mean of each of the samples and square the results. For the example, we have:

      (8 - 5)^2 = (3)^2 = 9

      (4 - 5)^2 = (-1)^2 = 1

      (3 - 5)^2 = (-2)^2 = 4

    • 3). Sum the squares and divide by one less than the number of samples. In the example, we have:

      (9 + 1 + 4)/(3 - 1)

      = (14)/2

      = 7

      This is the variance of the data.

    • 4). Compute the square root of the variance to find the standard deviation of the sample. In the example, we have standard deviation = sqrt(7) = 2.65.

    • 5). Divide the standard deviation by the square root of the number of samples. In the example, we have:

      2.65/sqrt(3)

      = 2.65/1.73

      = 1.53

      This is the standard error of the sample.

    • 6). Compute the relative standard error by dividing the standard error by the mean and expressing this as a percentage. In the example, we have relative standard error = 100 * (1.53/3), which comes to 51 percent. Therefore, the relative standard error for our example data is 51 percent.

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