91Ó°ÊÓ

The possible sample means cluster increasingly closely around the population mean as the sample size grows. That is, sample means for a higher sample size are less deviated from the population mean than sample means for a smaller sample size. As a result, as the sample size grows, the standard deviation of the sample means reduces, because the standard deviation of a set of observations is actually the root mean square departure of the observations from the mean value.

We calculate the population mean using the sample mean. i.e., we pick a sample at random from all feasible samples of a given size and use the sample mean to estimate the population mean. So, if sample means are close to the population mean for a particular sample size (i.e., the S.D. of sample means is small), we are more likely to achieve a decent estimate of the population mean, i.e., we estimate the population mean with less sampling error. As a result, when the population is estimated using a sample mean with a larger sample size, one should expect a good estimate.