# Do you need to report the standard error of the mean when the sample is the population?

The other day, my tutor told me that whenever a mean value is reported, the standard error of the mean must be reported alongside. But surely this isn't always the case? For example, let's say we calculate the mean number of goals a football team scores per game across a season. We're not sampling from a population in this case - the number of goals the team scores is the population. Am I right in saying the standard error would not need to be reported in this case?

• Can you explain further why you don't want to include the std when you have all the population? – tashuhka Aug 2 '14 at 11:55
• @tashuhka: In this case, the sample mean is a 100% precise estimate of the true average. There is no sampling error here or other sources of error, thus no clear reason to add standard errors. Standard deviation of course would add useful information though. – Michael M Aug 2 '14 at 15:01

The other day, my tutor told me that whenever a mean value is reported, the standard error of the mean must be reported alongside.

"Must"? I don't think so. Perhaps your tutor meant within some particular context. On the other hand, it's nearly always a good idea.

the number of goals the team scores is the population.

If you have the population, the standard error is simple to calculate.

Am I right in saying the standard error would not need to be reported in this case?

If it's known that you have the population, I wouldn't have thought it was necessary to say "the standard error is 0, since we have the population".

I applaud the encouragement to include standard errors, but if the statement that it must always be done was intended to apply completely generally, it seems a bit overblown.