Reasoning and Sense Making with Data Analysis T ANKS, P LANES, AND UNICEF Math Olympiad 2011 Northwest Missouri State University Neil Hatfield

S TATISTICAL P ROBLEM S OLVING  Formulating a question (questions) that can be addressed with data.  Designing and employing a plan for data collection.  Analyzing and summarizing that data.  Interpreting the results from the analysis, and answering the question(s) on the basis of the data. NCTM (2000) and Guidelines for Assessment and Instruction in Statistics Education (2007)

R EASONING AND S ENSE M AKING  Common Thread: Focus on making sense of and reasoning about the variation in data.  “Why is our data not all the same?”  Data Analysis  Modeling Variability  Connecting Statistics and Probability  Interpreting Designed Statistical Studies

D ATA A NALYSIS  Gaining insight about a solution to a statistics question by  Collecting Data  Describing Features of the Data  Using Graphical and Tabular Representations  Numerical Summaries

M ODELING V ARIABILITY  Developing probability models to describe the long-run behavior of observations of a random variable.  The design and implementation of a simulation provides transitional steps in the development of reasonable mathematical models for describing the long-run behavior of a random variable.

C ONNECTING S TATISTICS AND P ROBABILITY  By incorporating randomness, probability provides a way to make sense of the variation in the sample.  Sampling distribution of a sample statistic summarizes the long-run behavior of the statistic from repeated random sampling.  Sampling distributions make crucial links among data analysis, probability, and inferential reasoning in statistics.

C ONNECTING S TATISTICS AND P ROBABILITY Picture(s) Analysis “Statistics” Data Probability Random Sampling Variation Sampling Distribution Long Term Inference

I NTERPRETING D ESIGNED S TATISTICAL S TUDIES  Students should understand that the scope of inference for a study is related to the manner in which the data are collected.  Sampling distributions offer a way to quantify the uncertainty associated with statistical inference.  The reasoning employed in statistical inference is often quite difficult for students  Using a simulation to create a sampling distribution offers an intuitive way to help students develop this reasoning.

T HREE A CTIVITIES  Tanks: How Statistics Won World War IIHow Statistics Won World War II  Variation of the famous World War II German Tank Problem.  Planes: Where to Put the Armor?Where to Put the Armor?  World War II British Bombers (Operations Research)  UNICEF: What Does It Show?What Does It Show?  Deceptive Statistics

T ANKS H OW S TATISTICS W ON W ORLD W AR II  Formulating a question or questions:  Done for the students, initially; homework  Designing and Employing a plan for data collection.  Data Analysis—drawing random samples  Analyzing and summarizing the data.  Data Analysis—finding statistics  Modeling Variability—determining variance  Interpreting the results from the analysis.  Connecting Statistics and Probability—randomness, simulation, bias  Interpreting Studies—how to choose a good estimator

P LANES W HERE TO P UT THE A RMOR ?  Formulating a question or questions:  Question Analysis—is it really the right question?  Designing and Employing a plan for data collection.  Data Analysis—collecting the right data, biased data  Analyzing and summarizing the data.  Data Analysis—finding statistics  Modeling Variability—determining variance  Interpreting the results from the analysis.  Connecting Statistics and Probability—simulation, biased data  Interpreting Studies—answering the question with the right data

UNICEF W HAT D OES I T S HOW ?  Formulating a question or questions:  Question Analysis—What is the question?  Designing and Employing a plan for data collection.  Data Analysis—Where did they get their data?  Analyzing and summarizing the data.  Data Analysis—What do their summaries really tell us?  Data Analysis—What are graphs really honest?  Interpreting the results from the analysis.  Interpreting Studies—Does the data support what they said?

P URPOSE  Reasoning and Sense Making  Data Analysis  Get students to think critically about the world around them.

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