Census
A census is a study that collects data from every member of an entire population rather than a sample.
Definition
A census is when you collect information from every single person or thing in a group, not just a sample, a complete enumeration of an entire population as opposed to a sample survey. Because it measures the whole population, a census produces parameters directly rather than estimates; however, censuses are costly, slow, and prone to undercounting. Census errors include coverage error (missing units), nonresponse error, and measurement error, and agencies like the U.S. Census Bureau use statistical methods including dual-system estimation (capture-recapture) to correct undercounts.
Example
The United States government conducts a census every $10$ years, trying to count and gather information from every person living in the country. A small company with $25$ employees surveying all $25$ about job satisfaction is also conducting a census, so the resulting average satisfaction score is a population parameter, not an estimate. Dual-system estimation treats the census and a post-enumeration survey as two independent samples: if $N^*$ is the corrected population estimate, $N^* = (n_1 \times n_2)/m$, where $n_1$ and $n_2$ are the sizes of each count and $m$ is the number of matches.
Key Insight
A census gives you the most complete picture, but it is also the most expensive and time-consuming approach, which is why samples are often used instead. Even a census has errors: some people refuse to respond, some cannot be reached, and some are counted twice, so a well-designed sample can sometimes be more accurate than a flawed census. The apparent simplicity of "count everyone" conceals significant statistical complexity: perfect enumeration of a large, mobile, heterogeneous population is practically impossible, making statistical adjustment methods essential.