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Chapter4Bwd

# Chapter4Bwd - 192 Chapter Number and Title ction New York...

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192 Chapter Number and Title CARL FRIEDRICH GAUSS The Gaussian Distributions By age 18, Carl Friedrich Gauss (1777–1855) had indepen- dently discovered the binomial theorem, the arithmetic- geometric mean, the law of quadratic reciprocity, and the prime-number theorem. By age 21, he had made one of his most important discoveries: the construction of a regular 17-sided polygon by ruler and compasses, the first advance in the field since the early Greeks. Gauss’s contributions to the field of statistics include the method of least squares and the normal distribution, frequently called a Gaussian distribution in his honor. The normal distribution arose as a result of his attempts to account for the variation in individual observations of stellar locations. In 1801, Gauss predicted the position of a newly discovered asteroid, Ceres. Although he did not disclose his methods at the time, Gauss had used his least-squares approximation method. When the French mathematician Legendre published his version of the method of least-squares in 1805, Gauss’s response was that he had known the method for years but had never felt the need to publish. This was his frequent response to the discoveries of fellow scientists. Gauss was not being boastful; rather, he cared little for fame. In 1807, Gauss was appointed director of the University of Göttingen Observatory, where he worked for the rest of his life. He made important discoveries in number theory, algebra, conic sections and elliptic orbits, hypergeometric functions, infinite series, differ- ential equations, differential geometry, physics, and astronomy. Five years before Samuel Morse, Gauss built a primitive telegraph device that could send messages up to a mile away. It is probably fair to say that Archimedes, Newton, and Gauss are in a league of their own among the great mathematicians. Gauss’s contributions to the field of statistics include the method of least-squares and the normal distribution, frequently called a Gaussian distribution in his honor. The Granger Collection, New York

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c h e r a p t 4 More on Two-Variable Data 4.1 Transforming Relationships 4.2 Cautions about Correlation and Regression 4.3 Relations in Categorical Data Chapter Review
194 Chapter 4 More on Two-Variable Data ACTIVITY 4 Modeling the Spread of Cancer in the Body Materials: a regular six-sided die for each student; transparency grid; copy of grid for each student Cancer begins with one cell, which divides into two cells. 1 Then these two cells divide and produce four cells. All the cancer cells produced are exactly like the original cell. This process continues until there is some intervention such as radi- ation or chemotherapy to interrupt the spread of the disease or until the patient dies. In this activity you will simulate the spread of cancer cells in the body.

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