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Statistics is a branch of mathematics working with data collection, organization, analysis, interpretation and presentation. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people 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.See glossary of probability and statistics.Some definitions are:The earliest writing on statistics was found in a 9th-century book entitled Manuscript on Deciphering Cryptographic Messages, written by Arab scholar Al-Kindi (801–873). In his book, Al-Kindi gave a detailed description of how to use statistics and frequency analysis to decipher encrypted messages. This text laid the foundations for statistics and cryptanalysis. Al-Kindi also made the earliest known use of statistical inference, while he and other Arab cryptologists developed the early statistical methods for decoding encrypted messages. Arab mathematicians including Al-Kindi, Al-Khalil (717–786) and Ibn Adlan (1187–1268) used forms of probability and statistics, with one of Ibn Adlan's most important contributions being on sample size for use of frequency analysis.When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models. The idea of making inferences based on sampled data began around the mid-1600s in connection with estimating populations and developing precursors of life insurance.A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.Misuse of statistics can produce subtle, but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.Applied statistics comprises descriptive statistics and the application of inferential statistics. Theoretical statistics concerns the logical arguments underlying justification of approaches to statistical inference, as well as encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.Statistical techniques are used in a wide range of types of scientific and social research, including: biostatistics, computational biology, computational sociology, network biology, social science, sociology and social research. Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:

[ "Mathematics", "Cramér–Wold theorem", "Next-bit test", "Warped linear predictive coding", "Carelessness", "stochastic independence" ]
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