Census

In a census you record data on every individual in the population, so what you compute is the parameter and not an estimate of it. There is no sampling distribution around it, no standard error, no margin of error, because nothing was sampled. What makes a study a census is coverage of the population as you defined it, which means the same set of responses can be a census of one group and a sample of a larger one.

A department has 8 teachers with 3, 5, 6, 8, 11, 12, 14, and 21 years of experience. If the population is that department, the mean $\frac{80}{8} = 10$ years is $\mu$ (mu), exact and final: no interval is needed because no other value is possible. Ask instead about all teachers in the district and those 8 become a sample, the same 10 years becomes $\bar{x}$ (x-bar), and it turns into an estimate carrying uncertainty. The arithmetic did not move. The population did.

"A census has no error" holds for exactly one kind of error. It removes sampling error, the sample-to-sample variation that exists because you measured a part instead of the whole. Every other flaw survives: households an enumerator never reaches are undercoverage, people who refuse at the door are nonresponse, and a leading question produces the same response bias at full coverage that it produces in a sample of 300.

There is also nothing left to infer. When the data cover the population of interest, a confidence interval has no unknown parameter to bracket and a significance test has no population claim to weigh. If two fully measured departments average 10 and 11.4 years of experience, that 1.4 year gap is a description of those two departments, and testing it for significance answers a question nobody needed to ask.

A census is rare for practical reasons rather than statistical ones: cost, time, populations that change while you count them, and measurements that destroy what they measure, since testing every battery until it fails leaves none to sell.