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Introduction
In statistics, Karl Pearson's (1857–1936) method of moments unified the arithmetic mean, the standard deviation, and a number of further statistical calculations. It may be surprising to learn that the underlying concepts of the method of moments come from physics. For Karl Pearson, though, this development was a natural one.
After introducing the story of Karl Pearson's journey to the study of statistics, we present a set of practical data values which can be analyzed directly or grouped into classes and then analyzed. As we obtain the mean and standard deviation of this data set, we will see how the physics of the first and second moments aid in our computations, and of even more importance, give us insights into the results of the calculations.
Karl Pearson: Historical preliminaries
Even though Karl Pearson has been heralded as “the founder of the twentieth century science of statistics” [2, p. 447], his story had a much different beginning. Carl Pearson (as he was christened) grew up in an upper middle class Victorian London home. In 1875, Carl earned a scholarship at King's College, Cambridge, where he studied the works of Charles Darwin (1809–1882) and of Benedict Spinoza (1632–1677), and German history. He graduated with honors in mathematics (1879). After graduation, Pearson traveled and studied in Germany, where he became so enamored with the works of Karl Marx that he changed the legal spelling of his name from Carl to Karl; to his friends and colleagues, he was also known as K.P. When he returned to London, he was admitted to the bar (1881), and as his father wished, he practiced law for a short time.
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