Anyone committed to empirical observation as a means of knowing the universe about us can apply statistics as a research tool. This obviously includes science but includes history and the arts as well. For example, econometrics makes heavy use of applied statistics to study the economy.
In each of these areas, we need to observe, recognize the potential for error in our observations, and plan our research to control the observational error.
Statistics is a broad mathematical discipline which studies ways to collect, summarize and draw conclusions from data.
In contrast, mathematical statistics (or simply statistical theory) is the subdiscipline of applied mathematics which uses probability theory and analysis to place statistical practice on a firm theoretical basis.
The word statistics is also the plural of statistic (singular), which refers to the result of applying a statistical algorithm to a set of data.
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