Census
Statistics & ProbabilityA 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. It gives you exact information about the whole population.
Example
The United States government conducts a census every $10$ years, trying to count and gather information from every person living in the country.
Key Insight
A census gives you the most complete picture, but it is also the most expensive and time-consuming approach. That is why we often use samples instead.
Definition
A census is a complete enumeration of an entire population, as opposed to a sample survey. Because it measures the whole population, a census produces parameters directly, not estimates. However, censuses are costly, slow, and prone to undercounting.
Example
A small company with $25$ employees surveys all $25$ about job satisfaction. Since every employee is included, this is a census, and the resulting average satisfaction score is a population parameter, not an estimate.
Key Insight
Even a census has errors: some people refuse to respond, some cannot be reached, and some are counted twice. A well-designed sample can sometimes be more accurate than a flawed census.
Definition
A census attempts to achieve complete coverage of a finite population $N$. Census errors include coverage error (missing units), nonresponse error, and measurement error. The U.S. Census Bureau uses statistical methods including dual-system estimation (capture-recapture) to correct undercounts.
Example
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
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.