What is the sampling distribution of the mean?

The distribution of these means, or averages, is called the "sampling distribution of the sample mean". This distribution is normal (, /) (n is the sample size) since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not (see central limit theorem). read more

Since the mean is 1/N times the sum, the variance of the sampling distribution of the mean would be 1/N 2 times the variance of the sum, which equals σ 2 /N. The standard error of the mean is the standard deviation of the sampling distribution of the mean. read more

The sampling distribution of the (sample) mean is also called the distribution of the variable \(\bar{y}\). Usually, the sampling distribution of the sample mean is complicated except for very small sample size or for large sample size. read more