Fundamentals of Statistics
Syllabus and Sample Activity
Create a Sampling Distribution
Each student obtains and calculates the mean for eight different simple random samples of size 4 from a population of exam grades. The class constructs a histogram of sample means to illustrate a sampling distribution. The teacher demonstrates a sampling distribution from the same population using sample size n=2. Students consider the sampling distributions of sample means and the population distribution in light of the purpose of statistics, i.e., to make inferences about the population from sample data.
Note about the Central Limit Theorem
It is not practical to use this lesson to illustrate the Central Limit Theorem because students would have to calculate the means of multiple samples with n=25 or more. The more difficult concept here is the sampling distribution itself. This activity lays a strong foundation for students to understand the Central Limit Theorem by illustrating what a sampling distribution is. I then use computer simulations to illustrate the Central Limit Theorem in the next lesson.
Lesson Files
Activity Worksheet
LessonPlan
Sampling Distributions Power Point
Sample Histogram
Research Project
For the project outlined below, students, individually, conduct research consisting of a survey or experiment. To complete the project, students gather the appropriate data for exploratory data analysis and perform the analysis summarizing the data using the descriptive tools from the course. A formal report of the project is to be typed and submitted as if it were a scientific paper ready for presentation. The project is graded as follows:
- Description (10%) A typed, double-spaced, one-page description of the question the student wishes to address and his or her plan for gathering data.
- Draft (30%) A typed, double-spaced draft of the project that includes the Introduction, Methodology, and Data Exploration sections outlined below in the Project Outline.
- Final (60%) A typed, double-spaced final report incorporating any suggested changes to the draft and the remaining sections—Results, Conclusion, and Future Study—as outlined below in the Project Outline.
Project Outline
- Introduction - Describe the project and scope of the problem addressed.
- Methodology - Provide any details of the approach to the problem solution. State methods of data gathering, difficulties, assumptions and/or constraints, and the statistical analyses/tests used.
- Data Exploration - Provide both graphic and numeric summaries of the data and document the data exploration with explanations of any and all calculations used. Provide tabular results in an appendix to the report.
- Results - Provide calculations and results of statistical tests/inferences.
- Conclusion - Provide a clear rationale of the conclusion(s) reached in this project.
- Future Study - In a project of this nature [with time being a factor to properly complete a full investigation of a question/project] provide a description of what should be included in further study of the problem.