Course Overview
Overarching Enduring Understandings for the course
- Mathematics is a useful language for symbolically modeling and thus simplifying and analyzing our world.
- Mathematics is a logical and objective means of analyzing and solving problems.
- The effective communication of mathematics is essential to its application.
Topical Enduring Understandings for the course
- Students will understand that statistical information is a powerful, pervasive force in our world.
- Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns.
- Data must be collected according to a well-developed plan if valid information is to be obtained.
- Probability is the tool used for anticipating what the distribution of data should look like under a given model.
- Statistical inference guides the selection of appropriate models.
- Students will understand that statistics can be used to make valuable, reliable inferences from empirical information.
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Unit 1 - Exploring Univariate Data |
- How do we communicate data?
- How do we understand data?
- Can you lie with statistics? How and to what extent?
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Unit 2 – Exploring Bivariate and Categorical Data |
- To what extent can we predict the future?
- Is correlation ever causation?
- How can modeling data help us to understand patterns?
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Unit 3 – Planning and Conducting Studies and Experiments |
- How do we obtain data?
- To what extent is all data biased?
- To what extent does data collection methodology affect results?
- How can variable be eliminated through randomization?
- How does one decide between an observational study, an experiment, and a simulation?
- To what extent can data be purposefully biased?
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Unit 4 – Probability and Random Variables |
- When is probability a sure thing?
- How can we base decisions on chance?
- What is a random variable?
- How may random variables be combined?
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Unit 5 – Binomial, Geometric, and Sampling Distributions |
- How can modeling predict the future?
- To what extent does our world exhibit binomial and geometric phenomena?
- How do sampling distributions relate to population distributions?
- What is a normal distribution?
- How does the normal distribution apply to the real world?
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Unit 6 – Introduction to Inference |
- What is inference?
- How can decisions be based on chance?
- To what extent should decisions be based on chance?
- How can we determine the mean of a population with a “small” sample?
- When are tests of significance and confidence intervals used?
- How can one prepare for errors from significance tests?
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Unit 7 – Inference for means and proportions |
- How can we determine the mean of a population with a “small” sample?
- To what extent are significance tests reliable?
- How can we determine the mean of a population with a “small” sample?
- To what extent are significance tests reliable?
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Unit 8 – Inference for Goodness of Fit, Independence, and Regression |
- How can we test a series of proportions?
- How can we verify that two variables are independent?
- How can we test the slope of a correlation?
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Unit 9 – Review |
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Unit 10 – Final Project |
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