Therefore, the sum of the squared deviations is 98 (36 + 4 + 9 + 49). Next, calculate the sum of the squared deviations of each sample value from the mean (Steps 2-4).Calculate the mean of these values by adding them together and dividing by 4.The values in your sample are 52, 60, 55, and 65. Subtracting the standard error from the mean / adding the standard error to the mean will give the mean ± 1 standard error.This results gives you the standard error. Divide the standard deviation by the square root of the sample size (n).This result gives you the standard deviation. Calculate the square root of the value obtained from Step 5.Divide the sum of the squared deviations by one less than the sample size (n-1).

Add the squared deviations from Step 3.

Calculate each measurements deviation from the mean.

Calculate the mean of the total population.

Standard error is calculated by dividing the standard deviation of the sample by the square root of the sample size. Standard error decreases when sample size increases because having more data yields less variation in your results. Standard error increases when standard deviation increases. On the other hand, a smaller standard error indicates that the means are closer together, and thus it is more likely that your sample mean is an accurate representation of the true population mean. Standard error estimates how accurate the mean of any given sample represents the true mean of the population.Ī larger standard error indicates that the means are more spread out, and thus it is more likely that your sample mean is an inaccurate representation of the true population mean. The standard deviation of this distribution of sampling means is known as the standard error. When you take samples from a population and calculate the means of the samples, these means will be arranged into a distribution around the true population mean.

What it is, Why it Matters, and How to Calculate

Standard error of the mean