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Chapter Number and Title
CARL FRIEDRICH GAUSS
The Gaussian Distributions
Carl Friedrich Gauss (1777–1855)
had indepen
dently discovered the binomial theorem, the arithmetic
geometric mean, the law of quadratic reciprocity, and the
primenumber theorem. By age 21, he had made one of his
most important discoveries: the construction of a regular 17sided 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
leastsquares approximation method. When the French mathematician
Legendre published his version of the method of leastsquares 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
Gauss’s contributions to
the field of statistics
include the method of
leastsquares and the
normal distribution,
frequently called a
Gaussian distribution in
his honor.
The Granger Collection, New York
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4
More on TwoVariable 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 TwoVariable Data
ACTIVITY 4
Modeling the Spread of Cancer in the Body
Materials: a regular sixsided 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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This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.
 Fall '08
 O
 Binomial

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