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To find the standard error, first you must determine the standard deviation (because the standard deviation, s, is part of the standard error formula). Start by finding the average of your sample values. Sample mean is expressed as the arithmetic mean of measurements x1, x2, . . . xn. It is calculated with a formula that is shown above. For example, say you need to calculate the standard error of a sample mean for the weight measurements of five coins, as listed in the table below:You would calculate the sample mean by plugging the weight values into the formula, like this: Once you have the sample mean, you can expand your table by subtracting it from each individual measurement, then squaring the result. In the example above, your expanded table would look like this: The total deviation is the average of these squared differences from the sample mean. Add your new values together to determine it. In the example above, you would calculate as follows:This equation gives you the total quadratic deviation of measurements from the sample mean. Note that the sign of the differences is not important. Once you know the total deviation, you can find the average deviation by dividing by n -1. Note that n is equal to the number of measurements. In the example above, you have five measurements, so n 1 would equal 4. You would calculate as follows: You now have all the necessary values to use the formula for standard deviation, s. In the example above, you would calculate standard deviation as follows:Your standard deviation is therefore 0.0071624.
Calculate the sample mean. Subtract the sample mean from each measurement and square the value. Find the total deviation of your measurements from the sample mean. Calculate the average quadratic deviation of your measurements from the sample mean. Find the standard deviation.