Question

Calculate the standard error, given a population of 250, sample size 50 and population standard deviation of 25.

Answer 1

Use standard error formula 
$\text{standard error} = \dfrac{\sigma}{\sqrt{n}}$

where $\sigma = \text{population standard deviation}$
$n = \text{sample size}$

Answer 2

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.