The standard error of the mean or SEM it is called is estimated by the following formula:
SEM = σ / √n where σ = standard deviation of the population and n is the number of elements in the sample taken. ie., the sample size.
If the standard deviation of the population is not available then, we use the standard deviation of the sample, this is another way of estimating the standard error.
SEM = 25/√50 = 3.53
So the population mean is supposed to be within the mean of the sample + or - of 3.53. So we know the mean of the sample, then we say with some confidence that the population mean lies within this range.
Normally we use the standard deviation of the sample and not the population to estimate the SEM.