Book contents
- Frontmatter
- Preface
- Contents
- 1 The Sources of Algebra
- 2 How to Measure the Earth
- 3 Numerical solution of equations
- 4 Completing the Square through the Millennia
- 5 Adapting the Medieval “Rule of Double False Position” to the Modern Classroom
- 6 Complex Numbers, Cubic Equations, and Sixteenth-Century Italy
- 7 Shearing with Euclid
- 8 The Mathematics of Measuring Time
- 9 Clear Sailing with Trigonometry
- 10 Copernican Trigonometry
- 11 Cusps: Horns and Beaks
- 12 The Latitude of Forms, Area, and Velocity
- 13 Descartes' Approach to Tangents
- 14 Integration à la Fermat
- 15 Sharing the Fun: Student Presentations
- 16 Digging up History on the Internet: Discovery Worksheets
- 17 Newton vs. Leibniz in One Hour!
- 18 Connections between Newton, Leibniz, and Calculus I
- 19 A Different Sort of Calculus Debate
- 20 A ‘Symbolic’ History of the Derivative
- 21 Leibniz's Calculus (Real Retro Calc.)
- 22 An “Impossible” Problem, Courtesy of Leonhard Euler
- 23 Multiple Representations of Functions in the History of Mathematics
- 24 The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation
- 25 Finding the Greatest Common Divisor
- 26 Two-Way Numbers and an Alternate Technique for Multiplying Two Numbers
- 27 The Origins of Integrating Factors
- 28 Euler's Method in Euler's Words
- 29 Newton's Differential Equation ẏ/ẋ = 1 − 3x + y + xx + xy
- 30 Roots, Rocks, and Newton-Raphson Algorithms for Approximating √2 3000 Years Apart
- 31 Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras
- 32 Thomas Harriot's Pythagorean Triples: Could He List Them All?
- 33 Amo, Amas, Amat! What's the sum of that?
- 34 The Harmonic Series: A Primer
- 35 Learning to Move with Dedekind
- About the Editors
24 - The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation
- Frontmatter
- Preface
- Contents
- 1 The Sources of Algebra
- 2 How to Measure the Earth
- 3 Numerical solution of equations
- 4 Completing the Square through the Millennia
- 5 Adapting the Medieval “Rule of Double False Position” to the Modern Classroom
- 6 Complex Numbers, Cubic Equations, and Sixteenth-Century Italy
- 7 Shearing with Euclid
- 8 The Mathematics of Measuring Time
- 9 Clear Sailing with Trigonometry
- 10 Copernican Trigonometry
- 11 Cusps: Horns and Beaks
- 12 The Latitude of Forms, Area, and Velocity
- 13 Descartes' Approach to Tangents
- 14 Integration à la Fermat
- 15 Sharing the Fun: Student Presentations
- 16 Digging up History on the Internet: Discovery Worksheets
- 17 Newton vs. Leibniz in One Hour!
- 18 Connections between Newton, Leibniz, and Calculus I
- 19 A Different Sort of Calculus Debate
- 20 A ‘Symbolic’ History of the Derivative
- 21 Leibniz's Calculus (Real Retro Calc.)
- 22 An “Impossible” Problem, Courtesy of Leonhard Euler
- 23 Multiple Representations of Functions in the History of Mathematics
- 24 The Unity of all Science: Karl Pearson, the Mean and the Standard Deviation
- 25 Finding the Greatest Common Divisor
- 26 Two-Way Numbers and an Alternate Technique for Multiplying Two Numbers
- 27 The Origins of Integrating Factors
- 28 Euler's Method in Euler's Words
- 29 Newton's Differential Equation ẏ/ẋ = 1 − 3x + y + xx + xy
- 30 Roots, Rocks, and Newton-Raphson Algorithms for Approximating √2 3000 Years Apart
- 31 Plimpton 322: The Pythagorean Theorem, More than a Thousand Years before Pythagoras
- 32 Thomas Harriot's Pythagorean Triples: Could He List Them All?
- 33 Amo, Amas, Amat! What's the sum of that?
- 34 The Harmonic Series: A Primer
- 35 Learning to Move with Dedekind
- About the Editors
Summary
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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- Information
- Mathematical Time CapsulesHistorical Modules for the Mathematics Classroom, pp. 189 - 198Publisher: Mathematical Association of AmericaPrint publication year: 2011