what is sem in statistics

The standard error of the mean (SEM) is a measure of the variability of sample means in a sampling distribution of means. It is the standard deviation of the theoretical distribution of the sample means, which is the sampling distribution. SEM is used to estimate how far the sample mean is likely to be from the true population mean. SEM is calculated by taking the standard deviation and dividing it by the square root of the sample size. The precision of the sample mean as an estimate of the true population mean is quantified by SEM, and the precision increases as the sample size increases. Unlike standard deviation (SD), which quantifies variability, SEM quantifies uncertainty in the estimate of the mean. While SEM and SD are used interchangeably to express variability, they measure different parameters, and data should be precisely summarized with SD and not with SEM.