The standard error of the mean is a statistic that calculates how accurately a sample distribution represents a population using standard deviation.

Consider a group of feral cats in a neighborhood. Randomly sample five cats and note the mean weight and standard deviation. Repeating this a few more times with different cats from the same neighborhood, one can see each random sampling yields a slightly different mean and standard deviation.

The standard deviation of all these sample means is the standard error of the mean, expressed as sigma x bar. It represents the variation between the mean weight of the cats among different random samples.

The standard error of the sample means is calculated using this formula. Here, n represents the sample size and sigma is the population standard deviation.

Although the terms standard deviation and standard error are related, the standard deviation measures the variation within a sample. In contrast, the standard error of the mean measures the variation between the means of two or more samples from the same population.