Final answer:
The standard deviation of a sampling distribution is known as the standard error, and when referring to the sample mean, it is specifically called the standard error of the mean. It measures how much the sample mean is expected to vary from one sample to another and is a crucial concept in inferential statistics, particularly for estimating the precision of sample statistics.
Step-by-step explanation:
The standard deviation of a sampling distribution is called the standard error. Specifically, when we talk about the mean, it is known as the standard error of the mean. It is calculated using the formula σ/√n, where σ is the population standard deviation and n is the size of the sample. This measurement indicates how much the sample mean would vary if we repeatedly took samples from the same population.
The standard error reflects the sampling variability of a statistic and helps in estimating how precise a sample statistic (like the sample mean) is likely to be in comparison to the population parameter. The smaller the standard error, the more representative the sample mean is likely to be of the population mean.