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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities, government and business.

Statistical methods are used to summarize and describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics.

Statistics arose no later than the 18th century from the need of states to collect data on their people and economies, in order to administer them. The meaning broadened in the early 19th century to include the collection and analysis of data in general.

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Normal Distribution PDF.svg
Normal distribution probability density functions

The normal distribution or Gaussian distribution is a continuous probability distribution that describes data that clusters around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve.

The normal distribution can be used to describe, at least approximately, any variable that tends to cluster around the mean. For example, the heights of adult males in the United States are roughly normally distributed, with a mean of about 70 inches.

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Florence Nightingale 1920 reproduction.jpg
Florence Nightingale

Florence Nightingale, (1820 – 1910) was a pioneering nurse, writer and noted statistician. She became a pioneer in the visual presentation of information using statistical graphics such as pie charts and polar area diagrams. In her later life she made a comprehensive statistical study of sanitation in Indian rural life. In 1859 Nightingale was elected the first female member of the Royal Statistical Society and she later became an honorary member of the American Statistical Association.

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Anscombe's quartet
Credit: Schutz

Anscombe's quartet comprises four datasets which have identical simple statistical properties (mean, standard deviation, correlation, etc), yet which are revealed to be very different when inspected graphically. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician F.J. Anscombe to demonstrate the importance of graphing data before analyzing it, and of the effect of outliers on the statistical properties of a dataset.

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