Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse groups of individuals or objects such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with every aspect of data including the planning of data collection in terms of the design of surveys and experiments.
When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Sampling theory is part of mathematical statistics and relies on strong assumptions about the population being studied. However, many real-world populations are too complex for simple random sampling and require more sophisticated estimation strategies. The standard for measuring uncertainty due to sampling error was set by Ronald Fisher who defined variance as the square of the standard deviation when it was first introduced as a concept in his 1918 book The Correlation Between Relatives on the Supposition of Mendelian Inheritance. This definition was extended to include all typesests based on randomization in his 1925 book Statistical Methods for Research Workers.