This course is designed as a 4th year math credit for students seeking a class that prepares them for college courses that involve statistical reasoning. This 21st Century skill is a reflection of the increasingly data driven world we live in. This course will incorporate real-world applications for core statistical knowledge to better engage students in their learning. Students will be expected to work independently and in small and large groups to apply these concepts. Throughout this course; students will be required to communicate using mathematical and statistical vocabulary through giving oral and written analysis on multi-level statistical tests involving real-world context.
The primary focus of the class will be to teach students the basic principles of statistical reasoning; teaching students how to use four-steps of the statistical process: ask questions; collect data; analyze data; and make conclusions. Throughout the course; students will complete investigations that require students to complete the four-step statistical process to analyze real-world contexts. Major statistical topics include: analyzing distributions of univariate and bivariate data; both categorical and numerical; using graphs and summary statistics; correlation and least squares regression; using simulations to estimate probability distributions; theoretical probability distributions; including the binomial and normal distributions; rules of probability; including conditional probability and expected value; the logic of hypothesis testing; including stating hypotheses; calculating and interpreting p-values; drawing conclusions; and Type I and Type II errors; using confidence intervals to estimate parameters; and proper methods of data collection; including sampling and experimentation. The use of technology; including online applets and the graphing calculator will be prominent in the course.
Course goals and major student outcomes
* Students are able to formulate statistical questions and identify statistical claims made by others.
* Students can collect appropriate data to answer statistical questions; including designing experiments and using available data from the internet and other sources.
* Students can use a wide variety of tools to analyze and summarize distributions of data.
* Students understand the role of variability in the data collection process and incorporate this understanding when drawing conclusions about statistical questions.
* Students critically reflect on their own conclusions and conclusions made by others; including the limitations of these conclusions.
Students will be able to:
* Ask statistical questions and decide which type of data collection procedure is most appropriate in a given situation
* Collect data using online databases in an efficient and effective manner
* Describe the importance of random sampling and the difference between samples and populations
* Design experiments and understand the purpose of control; randomization; replication; and blinding
* Explain how using paired data can provide better results in experiments and observational studies
* Understand when it is appropriate to conclude that changes in one variable cause changes in another variable
* Critically reflect on the limitations of their own conclusions and conclusions made by others
* Summarize distributions of data with appropriate visual displays; including pie charts; bar charts; segmented bar charts; dotplots; histograms; boxplots; and timeplots
* Calculate and interpret summary statistics for numerical data; including the mean; median; range; quartiles; interquartile range; mean absolute deviation and standard deviation.
* Identify unusual values (outliers) in a distribution and understand their effect on summary statistics
* Compare distributions of numerical data; including comparisons of shape; center and spread.
* Use standardized scores to compare athletic performances measured on different scales
* Summarize the relationship between two quantitative variables; using scatterplots; the correlation coefficient; least squares regression lines; and standard deviation of the residuals; and how these measures are affected by unusual values (outliers)
* Explain the principle of least squares
* Describe the concept of regression to the mean
* Design and conduct simulations to estimate probability distributions; by hand and with technology
* Describe the law of large numbers and its role in simulation
* Explain the concept of independence
* Use the Normal distribution and binomial distribution to estimate probabilities
* Describe the relationship between statistics and parameters in real-world context
* Explain the concept of sampling variability in real-world context and its role in the decision making process
* State hypotheses; including a null and alternative hypothesis; about a single proportion; the difference between two proportions; independence of real-world context; the difference between two means or medians; the mean difference; the difference between two standard deviations; the correlation coefficient; and the slope of a least squares regression line
* Use hands-on methods and technology to simulate the distribution of a single proportion; the difference between two proportions; the difference between two means or medians; the mean difference; the difference between two standard deviations; the correlation coefficient; and the slope of a least squares regression line
* Estimate and interpret p-values using the results of simulations
* Use p-values to make appropriate conclusions about hypotheses
* Describe a Type I and Type II error in the context of a study and how to reduce the probability that they occur
* Calculate and interpret a confidence interval for a single proportion; a single mean (or mean difference); the difference between two proportions; and the difference between two means
* Use confidence intervals to make decisions
School countryUnited States
School / district Address500 W. Galveston St
School zip code85225
Requested competency codeMath
Approved competency code
- 4 years of Math