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From mean error to standard error

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To fully appreciate the math we are about to discuss, we must first rewind our clock to 1911. Udny Yule was enrolled into University College London at the young age of 16, where he remained from 1887 to 1890. Among his teachers were Karl Pearson (then Professor of Applied Mathematics), Alexander Kennedy (Professor of Engineering), J. A. Fleming (Professor of Electrical Engineering), J. M. Hill (Professor of Mathematics), C. Foster (Professor of Physics). While Yule was working with Heinrich Hertz in Bonn, Pearson offered him a role as demonstrator at UCL which he accepted, and he occupied this position from 1893 to 1896 (the year he was promoted to Assistant Professor of Applied Mathematics). 1911 is an important year for students of statistics. For one, the world's first statistics department was founded by Karl Pearson (1857 – 1936) in UCL. And two, the world's first G. U. Yule (1917) An introduction to the theory of statistics , 4th edit...

First demo of the method of moment by Pearson in 1893

In 1887, John Venn published a letter John Venn (1887) The law of error, Nature 36(931), pp. 411 - 412 (September 1, 1887) in Nature criticising Adolphe Quetelet (1796 - 1874) for naively believing that normal distribution is the only viable probability density function in nature. Venn's opening paragraph is reproduced as follows: Everyone interested in the theory of statistics is aware how strongly Quetelet was under the conviction that there is only one law of error prevalent for the departure from the mean of a number of magnitudes or measurements of any natural phenomonon. I have done what I can to protest against this doctrine as a theoretic assumption; and recently Galton and Edgeworth have shown how untenable it is, and how great is the importance of studying the properties of other laws of error than the symmetrical binomial, and its limiting form the exponential. Karl Pearson supported the notions of Venn and Galton an...