- Students should be provided opportunities to collect data of their own design (primary) and/or use data that already exists (secondary).
- Students should be able to critique studies of different design types and explain how randomization relates to each style of investigation.
- Students might design and carry out a study with a recognition of error in the design of the study.
- Students might evaluate a research study and critique the investigative measures and/or conclusions drawn from the data.
- Students should be able to question how data were collected, rationale for the study, positionality of the researcher, subjectivity of human decision making, etc.
- Students should be able to recognize bias and describe its potential effects. They do not need to memorize definitions of types of bias.
- Students might be provided opportunities to search for data on the internet and prepare it by implementing strategies for dealing with messy data.
- Students might be provided opportunities to search for data on the internet and then provide a critical evaluation of the methods used to collect, organize and communicate that data to the public.
- Messy data includes missing values, incorrect inputs, lack of representativeness, difficult formatting, etc.
- Students should be able to communicate statistical information using written and oral reports.
- Students should recognize that it is most often not feasible to study an entire population distribution. Therefore, students should have opportunities to explore representative samples from the population to make inferences concerning the population.
- Students should demonstrate understanding of how sampling distributions developed through simulation are used to describe the sample-to-sample variability of sample statistics.
- Students should summarize results from statistical analyses using appropriate statistical justifications that indicate an understanding of the statistics.
- Students should have many opportunities to communicate quantitative information using statistical language in oral, written, and graphical form to build data fluency.
- Students should understand that z-scores are a statistical tool that allows someone to compare samples with differing units. Students should have opportunities to use z-scores to make decisions when analyzing real-world data.
- Students should understand that z-scores can be used with all distributions, regardless of shape.
- Students should use technology tools to calculate standard deviation when necessary to determine z-scores.
- Students might compare performance on SAT versus ACT despite the different scoring scales by using z-scores.
- Students should understand that there are data sets for which such a procedure is not appropriate because it is not normally distributed.
- Students should be encouraged to use tools such as calculators, spreadsheets, or tables to estimate areas under a normal curve.
- Students should be able to use simulations to decide if a specified model accurately reflects real outcomes.
- Students should be able to consider the sample-to-sample variability by using statistics from repeated samples of the same size.
- Students could involve a simulated sampling distribution for a sample mean or a sample population to decide if a specified model accurately reflects real outcomes.
- Students should be able to apply the margin of error to make conclusions about the reliability of statistical results.
- Students do not have to calculate the margin of error.
- Students might be provided opportunities to develop confidence intervals using simulations and technology, such as statistical applets.
- Students might compare exit poll data with two different margins of error to determine if the results are conclusive.
- Students might explore questions such as: “In a favorability poll, if a politician has a 52% approval rating ±5 points, can they claim that most people approve?”
Textbook Connections
Module 10
Lesson 1- Random Sampling and Bias
Lesson 2- Simulations
Lesson 3- Analyzing Population Data, Standard Deviation, Variance, Outlier
Lesson 4- Normal Distribution, Z-scores
Lesson 5- Population Parameters
Module 10
Lesson 1- Random Sampling and Bias
Lesson 2- Simulations
Lesson 3- Analyzing Population Data, Standard Deviation, Variance, Outlier
Lesson 4- Normal Distribution, Z-scores
Lesson 5- Population Parameters