Is it appropriate to put "error bars" on data when you have the full population? I have data on the large number of people who were applying to receive an award.  Everyone who applied must fill out a survey and specify their gender (although they can choose "prefer not to say").  My question: is it appropriate to put "error bars" on this data given that the survey was not a sample of the population, but rather the whole population?  (Any citations would be helpful.)

@Ben is of course right that there is no "error" if you have the full population. But at least colloquially, "error-bars" are not always referring to uncertainties comming from a incomplete sample. And just a single number is seldomly useful, even if it is "exact". Two examples:

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*If you say "$34.7$ percent of applicants were male", then that number is exact and should not have an error-bar. BUT: If your goal is to say something about gender-bias for example, the exact number itself is not sufficient. You need to add a line like "given the total number of applicants that we have, a deviation from a 'perfect' 50% by $\pm X$ is statistically expected without any bias existing". This number $X$ is not an error-bar of your data. But it can serve the same purpose: It informs the reader to what degree the first number you quote is meaningful.


*If you say "on average, the applicants are $34.7$ years old", it might again be less helpful to the reader as it could be. Saying "the mean age of applicants is $34.7$ years with a standard deviation of $4.6$" is much more useful. This second number is of course not an error-bar, but it serves the same purpose because it tells the reader a range of expected results, which is generally more helpful than one central result alone.
(After thinking about it, case (1) is essentially equivalent to the thing @Ben was referring to as "superpopulation")
