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Statistics used in standardized testing assessment are shown. Scatter plots are used in descriptive statistics to show the observed relationships between different variables. Statistics is a branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model.
Measurement processes that generate statistical data are also subject to error. Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis. Merriam-Webster dictionary defines statistics as «a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. Statistician Sir Arthur Lyon Bowley defines statistics as «Numerical statements of facts in any department of inquiry placed in relation to each other. Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics. Mathematical statistics is the application of mathematics to statistics.
In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as «all persons living in a country» or «every atom composing a crystal». This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize the population data.