How to calculate standard errors

The standard error indicates the propagation of the measurements within a data sample. It is the standard deviation divided by the square root of the size of the data sample. The sample may include data from scientific measurements, test results, temperatures or a series of random numbers. The standard deviation indicates the deviation of the values ​​of the sample from the mean of the sample. The standard error is inversely proportional to the size of the sample - the larger the sample, the smaller the standard error .

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one

Calculate the average of the data sample . The average is the average of the values ​​of the sample. For example, if the observations of an experiment over a period of four days during the year are 50, 58, 55 and 60 ºC, the average is 56 ºC: (50 + 58 + 55 + 60) / 4 = 55.75 ºC

two

Calculate the sum of the deviations and squares (or differences) each sample value from the mean. Keep in mind that multiplying negative numbers by themselves (or numbers squared) gives positive numbers. In the present example, the squared deviations: (55, 75 - 50) ^ 2, (55, 75 - 58) ^ 2, (55, 75 - 55) ^ 2 and (55, 75 - 60) ^ 2, the results being 33.06; 5.0.6; 0.56; 18.06 respectively. Therefore, the sum of the deviations squared is 56.74.

3

Find the standard deviation . Divide the sum of the squared deviations by the sample size minus one, and then find the square root of the result. In the example, the sample size is four. Therefore, the standard deviation is the square root of [56.74 / (4-1)], which is approximately 4.34.

4

Calculate the standard error, which is the standard deviation divided by the square root of the sample size. To conclude the example, the standard error is 4.34 divided by the square root of 4, or 4.34 divided by 2 = 2.17.