Descriptive Statistics

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The Descriptive Statistics course introduces many essential topics of statistics. The students learn how to produce data through surveys, experiments, and observational studies. They then analyze the data through graphical and numerical summaries. The students next learn to model data, using basic probability and sampling distributions. And, with time permitting, the students discover how to draw conclusions from data using confidence intervals and significance tests.

The students learn when and how to use technology to aid in solving statistical problems. Furthermore, they produce convincing oral and written statistical arguments, using appropriate terminology. Most importantly, they become critical consumers of published statistical results by heightening their awareness of ways in which statistics can be improperly used to mislead, confuse, and distort the truth.

Assessments will include group and individual projects, daily homework assignments, quizzes, and tests. Resources used throughout the course include textbooks, graphing calculators, Fathom, and addtional websites, including statistical applets and Gallup.

Units

Unit Essential Questions Content Skills and Processes
Unit 1: Analyzing Data
  • How can we display data?
  • How can we describe the center and spread of data?
  • What is the Normal Model?
  • Tables and charts
  • Histograms, stem plots, and box plots
  • Median and IQR
  • Mean and standard deviation
  • The Normal Model
  • Analyzing and creating charts and tables
  • Analyzing and creating histograms, stem plots, and box plots
  • Recognizing when it is appropriate to use mean and standard deviation, or median and IQR, to describe the center and spread
  • Using the 68-95-99.7 Rule
  • Finding z-scores
Unit 2: Linear Regression
  • What features do we look for in a scatterplot?
  • When is it appropriate to find correlation?
  • How do we find correlation?
  • How do we find the equation for linear regression?
  • Why doesn't correlation imply causation?
  • Scatterplots
  • The correlation coefficient and r-squared
  • The linear regression equation
  • Residuals
  • Recognizing from the scatterplot when it is appropriate to use linear regression
  • Using the calculator to find the correlation coefficient, r-squared, and the linear regression equation
  • Calculating residuals
Unit 3: Collecting Data
  • What are various types of sample surveys?
  • How do sample surveys, experiments, and observational studies differ?
  • What are the essential components of a good experiment?
  • Randomness
  • Simple random samples, stratified samples, and cluster samples
  • Experiments
  • Observational studies
  • Generating random numbers
  • Conducting SRS, stratified, and cluster sampling
  • Understanding the problems associated with censuses
  • Understanding the main components of experimental design, i.e., control, randomization, replication, and blocking
  • Understanding that only an experiment, rather than an observational study, can help to establish causation
Unit 4: Probability
  • What are the basic rules of probability?
  • What is a random variable?
  • What is expected value?
  • What are the geometric and binomial models?
  • What is a sampling distribution?
  • Addition and multiplication rules of probability
  • Conditional probability
  • Random variables
  • Expected value
  • Geometric and binomial models
  • Sampling distributions
  • Solving probability problems involving the use of addition, multiplication, and conditional probability rules
  • Using tables and tree diagrams to find probabilities
  • Understanding what a random variable is
  • Finding expected value of random variables
  • Using the geometric and binomial models to calculate probabilities by hand and using the calculator
  • Understanding the basic principles of sampling distributions
Unit 5: Inference
  • What is a confidence interval?
  • What is a margin of error?
  • How does one conduct an inference test for a proportion or a mean?
  • What is are Type I and Type II errors?
  • Confidence intervals for means and proportion
  • Margin of error
  • Inference tests for means and proportions
  • Type I and Type II errors
  • Finding a confidence interval for means and proportions
  • Calculating margin of error
  • Conducting inference tests for means and proportions
  • Understanding Type I and Type II errors and how to prevent them