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The standard error of the mean is calculated using the standard deviation and the sample size.įrom the formula, you’ll see that the sample size is inversely proportional to the standard error.

The standard error of the math scores, on the other hand, tells you how much the sample mean score of 550 differs from other sample mean scores, in samples of equal size, in the population of all test takers in the region. This number reflects on average how much each score differs from the sample mean score of 550. The standard deviation of the math scores is 180. In this case, the sample is the 200 students, while the population is all test takers in the region. Example: Standard error vs standard deviationIn a random sample of 200 students, the mean math SAT score is 550. In contrast, the standard error is an inferential statistic that can only be estimated (unless the real population parameter is known). The standard deviation is a descriptive statistic that can be calculated from sample data. The standard error estimates the variability across multiple samples of a population.The standard deviation describes variability within a single sample.Standard error and standard deviation are both measures of variability: Using a large, random sample is the best way to minimize sampling bias. You can decrease standard error by increasing sample size. A low standard error shows that sample means are closely distributed around the population mean-your sample is representative of your population. That’s because a sample will never perfectly match the population it comes from in terms of measures like means and standard deviations.īy calculating standard error, you can estimate how representative your sample is of your population and make valid conclusions.Ī high standard error shows that sample means are widely spread around the population mean-your sample may not closely represent your population.

With probability sampling, where elements of a sample are randomly selected, you can collect data that is likely to be representative of the population. However, even with probability samples, some sampling error will remain. Standard error matters because it helps you estimate how well your sample data represents the whole population. In statistics, data from samples is used to understand larger populations.