Statistics Motivation

Why Statistics is Not Why Statistics is Not Mathematics and Why We Mathematics and Why We

Should Care About Should Care About Teaching StatisticsTeaching Statistics

What is Statistics?What is Statistics?

Statistics is a science in my opinion, and it Statistics is a science in my opinion, and it is no more a branch of mathematics than is no more a branch of mathematics than are physics, chemistry, and economics; for are physics, chemistry, and economics; for if its methods fail the test of experience – if its methods fail the test of experience – not the test of logic – they are discarded.not the test of logic – they are discarded.

- John Tukey, 1962- John Tukey, 1962

Statistics in IndustryStatistics in Industry

Statistical thinking is a philosophy of Statistical thinking is a philosophy of learning and action based on the following learning and action based on the following fundamental principles:fundamental principles: All work is a system of interconnected All work is a system of interconnected

processes.processes. Variation exists in all processes.Variation exists in all processes. Understanding and reducing variation are Understanding and reducing variation are

keys to success.keys to success.

- The American Society for Quality- The American Society for Quality

Statistics is a Mathematical ScienceStatistics is a Mathematical Science

We use the singular We use the singular isis and not the plural and not the plural areare to to emphasize that statistics is a field of study, not emphasize that statistics is a field of study, not just a bunch of numbers.just a bunch of numbers.

We use We use mathematicalmathematical as an adjective because as an adjective because although statistics certainly makes use of much although statistics certainly makes use of much mathematics, it is a separate discipline and not a mathematics, it is a separate discipline and not a branch of mathematics.branch of mathematics.

We use the noun We use the noun sciencescience because statistics is because statistics is the science of gaining insight from data.the science of gaining insight from data.

- From “Some Important Comparisons between Statistics and Mathemaics, and Why Teachers Should - From “Some Important Comparisons between Statistics and Mathemaics, and Why Teachers Should Care” by Rossman, Chance, and Medina (2006).Care” by Rossman, Chance, and Medina (2006).

Statistics is NOT a Branch of Statistics is NOT a Branch of MathematicsMathematics

The book The book A History of MathematicsA History of Mathematics (second edition by Carl B. Boyer and (second edition by Carl B. Boyer and Uta C Merzbach) is the classic one-Uta C Merzbach) is the classic one-volume history of mathematics.volume history of mathematics.

Statistics is not even mentioned in Statistics is not even mentioned in the comprehensive index.the comprehensive index.

Statistical Thinking vs. Mathematical Statistical Thinking vs. Mathematical ThinkingThinking

Mathematics is, by and large, a Mathematics is, by and large, a deterministic way of thinking and the way deterministic way of thinking and the way mathematics is taught in schools in mathematics is taught in schools in America entrenches students into a America entrenches students into a deterministic way of viewing the deterministic way of viewing the quantitative world around them.quantitative world around them.


Statistics is, by and large, a probabilistic Statistics is, by and large, a probabilistic or stochastic way of thinking.or stochastic way of thinking.

Why is this important?Why is this important?


Science entered the nineteenth century Science entered the nineteenth century with a firm philosophical vision that has with a firm philosophical vision that has been called the clockwork universe… By been called the clockwork universe… By the end of the nineteenth century, the the end of the nineteenth century, the errors had mounted instead of errors had mounted instead of diminishing… By the end of the twentieth diminishing… By the end of the twentieth century, almost all of science had shifted to century, almost all of science had shifted to using statistical models… Popular culture using statistical models… Popular culture has failed to keep up with the scientific has failed to keep up with the scientific revolution.revolution.

- David Salsburg “The Lady Tasting Tea” (2001)- David Salsburg “The Lady Tasting Tea” (2001)


Statistics has its own tools and ways of Statistics has its own tools and ways of thinking, and statisticians are quite insistent thinking, and statisticians are quite insistent that those of us who teach mathematics that those of us who teach mathematics realize that statistics is not mathematics, realize that statistics is not mathematics, nor is it even a branch of mathematics. In nor is it even a branch of mathematics. In fact, statistics is a separate discipline with fact, statistics is a separate discipline with its own unique ways of thinking and its own its own unique ways of thinking and its own tools for approaching problems.tools for approaching problems.

- J. Michael Shaughnessy, “Research on Students’ Understanding of Some Big Concepts - J. Michael Shaughnessy, “Research on Students’ Understanding of Some Big Concepts in Statistics” (2006)in Statistics” (2006)


Mathematical thinking is deductive: the Mathematical thinking is deductive: the inference of particular instances by inference of particular instances by reference to a general law or principle. reference to a general law or principle.

““General to specific”General to specific”


Statistical thinking is inductive: the Statistical thinking is inductive: the inference of general laws from particular inference of general laws from particular instances. instances.

““Specific to general”Specific to general”

Why Should We Care About Why Should We Care About Teaching Statistics?Teaching Statistics?

1983 report 1983 report A Nation at RiskA Nation at Risk listed the primary listed the primary ingredients of mathematics education as follows:ingredients of mathematics education as follows:

The teaching of mathematics in high school should The teaching of mathematics in high school should equip graduates toequip graduates to Understand geometric and algebraic concepts;Understand geometric and algebraic concepts; Understand elementary probability and statistics;Understand elementary probability and statistics; Apply mathematics in everyday situations; andApply mathematics in everyday situations; and Estimate, approximate, measure, and test the Estimate, approximate, measure, and test the

accuracy of their calculations.accuracy of their calculations.


The The Principles and Standards for school Principles and Standards for school MathematicsMathematics (NCTM, 2000) states the (NCTM, 2000) states the following five major content strands that following five major content strands that are are essentialessential for school mathematics (k- for school mathematics (k-12):12): Number and operationsNumber and operations AlgebraAlgebra GeometryGeometry MeasurementMeasurement Statistics and probabilityStatistics and probability


The NCTM also recommends that The NCTM also recommends that statistics and probability occupy statistics and probability occupy approximately 20% of the curriculum approximately 20% of the curriculum (based on time) at each grade level from (based on time) at each grade level from kindergarten to 12kindergarten to 12thth grade. grade.


2004 report Ready or Not: 2004 report Ready or Not: Creating a High Creating a High School Diploma That CountsSchool Diploma That Counts from the American from the American Diploma Project lists the following quantitative Diploma Project lists the following quantitative competencies needed for high school graduates competencies needed for high school graduates to succeed in postsecondary education or in to succeed in postsecondary education or in high-performance, high-growth jobs centers:high-performance, high-growth jobs centers: Number Sense and Numerical OperationsNumber Sense and Numerical Operations AlgebraAlgebra GeometryGeometry Data Interpretation, Statistics and ProbabilityData Interpretation, Statistics and Probability


The The Principles and Standards for school Principles and Standards for school MathematicsMathematics (NCTM, 2000) states that (NCTM, 2000) states that instructional programs from instructional programs from prekindergarten through grade 12 should prekindergarten through grade 12 should enable enable allall students to – students to – formulate questions that can be addressed formulate questions that can be addressed

with data and collect, organize and display with data and collect, organize and display relevant data to answer them;relevant data to answer them;

select and use appropriate statistical methods select and use appropriate statistical methods to analyze data;to analyze data;

develop and evaluate inferences and develop and evaluate inferences and predictions that are based on data;predictions that are based on data;

understand and apply basic concepts of understand and apply basic concepts of probability.probability.

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Statistics Motivation