Standard deviation with sample size formula

In practice we will never have the luxury of seeing the behaviour of the sampling process in this way remember this is a computer simulation. However there is a way of estimating the standard deviation associated with the sampling process through a mathematical expression applied to the data from a single sample. This formula is given by sf s/n, where s is the sd from the sample and n is the sample size. 

The second component is the standard error of the mean, which quantifies the extent to which the process of sampling has mis-estimated the population mean. The standard error of the mean has the same meaning as in the case for normally distributed data - that is, the standard error describes the degree of uncertainty present in our assessment of the population mean on the basis of the sample mean. It is also the standard deviation of the sampling distribution of the mean for samples of size n. The smaller the standard error, the greater the certainty with which the sample mean estimates the population mean. When ri is very large the standard error is very small, and therefore the sample mean is a very precise estimate of the population mean. As we know the standard deviation of the sample, s, we can make use of the following formula to determine the standard error of the mean, SE ... 

This paper deals with the derivation and application of a formula for computing standard deviation (a,) of the per cent of a given size in random samples from a granular material with a known size distribution ... 

Standard error. A measure of the variability of a statistic from sample to sample. (As opposed to standard deviation which is a measure of variability for original observations.) Since repeated samples are not usually obtained, standard errors cannot be calculated directly. They can be calculated on the basis of a single sample using an appropriate model and the assumptions it requires. For example, on the assumption that a sample has been obtained by simple random sampling, the standard error of the mean will equal the standard deviation divided by the square root of the sample size. This particular assumption, which implies that variability between samples can be simply estimated with the help of variability within samples, is rarely valid, however, and this formula is often inappropriately used in clinical trials. In fact, it is a standard error to use it. 

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