According to Black (2017), the purpose of the standard error of the mean is to determine how well the sample that is being considered in statistical analysis will be representative of the overall population which is being studied. The standard error of the mean is calculated through taking the standard deviation of the population and dividing it by the square root of the sample size. This allows for an individual to estimate what the standard deviation from the mean that the population will have.

The standard error of the mean is based off of the Central Limit Theorem, which suggests that if there are multiple samples from the population that are studied, the mean of the samples should be roughly equal to the mean of the population as a whole. So as the sample being evaluated is increased in size, the mean which is calculated from the sample should become closer to the mean of the population as a whole. Black (2017) further suggests that for the Central Limit Theorem to be applicable, the sample size which is being evaluated should consist of at least 30 samples, where even larger samples are more representative of the population as a whole. One of the advantages with a large sample size is that the sample can be drawn from a population that is not actually normally distributed, and allow for analyzing that population.

One of the additional considerations to make in working with standard error is that it is inversely proportional to the size of the sample, where the error is reduced as the size is increased (Black, 2017). In conducting statistical analysis of a sample representing a population, one would need to compare the resources required for a larger sample size versus the presence of the standard error to determine how representative their sample will be of the population.

References:

Black, K. (2017). Business Statistics: For Contemporary Decision Making, (9th Edition). Hoboken, NJ: Wiley.

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