One way we analyze data is to look at measures of central tendency—mean, median, and mode. They are the tools to look at the information for the purpose of answering the question, “What is normal?” Understanding the measures of central tendency can help us make important life decisions. For example, averages can help us set goals or plan budgets. At the end of this lesson about central tendency, students will be able to recognize and apply the concepts of mean, median, and mode in real-life problems.
Students analyze economic data to better understand America’s middle class, its role in the economy, and its impact on economic growth. In this interactive lesson, students use media produced for How the Deck Is Stacked, and tables and graphs created from Pew Research Center and government data to examine household income and spending trends and the widening wealth gap between the upper and lower-income tiers. Interim assessments evaluate students’ ability to interpret data, make inferences, and justify conclusions. At the end of the lesson, students write an evidence-based essay on why a shrinking middle-class matters to the U.S. economy.
Statistics and sampling are important for human performance experiments. Students will learn several sampling types including census, random, stratified random, and convenience. Examples of real-life sampling and experimental design are also shown.
Note: This video is available in both English and Spanish audio, along with corresponding closed captions.
Learn about the origins and meaning of “p-value,” a statistical measure of the probability that has become a benchmark for success in experimental science, in this video from NOVA: Prediction by the Numbers. In the 1920s and 1930s, British scientist Ronald A. Fisher laid out guidelines for designing experiments using statistics and probability to judge results. He proposed that if experimental results were due to chance alone, they would occur less than 5 percent (0.05) of the time. The lower the p-value, the less likely the experimental results were caused by chance. Use this resource to stimulate thinking and questions about the use of statistics and probability to test hypotheses and evaluate experimental results.
Real-world examples demonstrate the benefits of histograms in this 10-minute video from the Against All Odds statistics series. Data visualization techniques help students understand the practical application of statistics in meteorology and in predicting traffic patterns. Hosted by Pardis Sabeti, this series walks students through understanding how statistics are used in everyday life.
This topic introduces different types of statistical studies (e.g., observational studies, surveys, and experiments) (S-IC.B.3). The role of randomization (i.e., random selection in observational studies and surveys and random assignment in experiments) is addressed. A discussion of random selection (i.e., selecting a sample at random from a population of interest) shows students how selecting participants at random provides a representative sample, thereby allowing conclusions to be generalized from the sample to the population. A discussion of random assignment in experiments, which involves assigning subjects to experimental groups at random, helps students see that random assignment is designed to create comparable groups making it possible to assess the effects of an explanatory variable on a response.
The distinction between population characteristics and sample statistics (first made in Grade 7) is revisited. Scenarios are introduced in which students are asked a statistical question that involves estimating a population mean or a population proportion. For example, students are asked to define an appropriate population, population characteristic, sample, and sample statistics that might be used in a study of the time it takes students to run a quarter mile or a study of the proportion of national parks that contain bald eagle nests.
In this topic, students use data from a random sample to estimate a population mean or a population proportion. Building on what they learned about sampling variability in Grade 7, students use simulation to create an understanding of the margin of error. In Grade 7, students learned that the proportion of successes in a random sample from a population varies from sample to sample due to the random selection process. They understand that the value of the sample proportion is not exactly equal to the value of the population proportion. In Algebra II, they use margin of error to describe how different the value of the sample proportion might be from the value of the population proportion. Students begin by using a physical simulation process to carry out a simulation. Starting with a population that contains successes (using a bag with black beans and white beans), they select random samples from the population and calculate the sample proportion. By doing this many times, they are able to get a sense of what kind of differences are likely. Their understanding should then extend to include the concept of margin of error. Students then proceed to use technology to carry out a simulation. Once students understand the concept of margin of error, they go on to learn how to calculate and interpret it in context (S-IC.A.1, S-IC.B.4). Students also evaluate reports from the media in which sample data are used to estimate a population mean or proportion (S-IC.B.6).
Note: Although this module is identified as Algebra II in the EngageNY curriculum, it corresponds to the Precalculus Alabama Course of Study.
This topic focuses on drawing conclusions based on data from a statistical experiment. Experiments are introduced as investigations designed to compare the effect of two treatments on a response variable. Students revisit the distinction between random selection and random assignment.
When comparing two treatments using data from a statistical experiment, it is important to assess whether the observed difference in group means indicates a real difference between the treatments in the experiment or whether it is possible that there is no difference and that the observed difference is just a by-product of the random assignment of subjects to treatments (S-IC.B.5). To help students understand how this distinction is made, lessons in this topic use simulation to create a randomization distribution as a way of exploring the types of differences they might expect to see by chance when there is no real difference between groups. By understanding these differences, students are able to determine whether an observed difference in means is significant (S-IC.B.5).
Students also critique and evaluate published reports based on statistical experiments that compare two treatments (S-IC.B.6). For example, students read a short summary of an article in the online New England Journal of Medicine describing an experiment to determine if wearing a brace helps adolescents with scoliosis. Then, they watch an online video report for the Wall Street Journal titled “BMW Drivers Really Are Jerks” that describes a study of the relationship between driving behavior and the type of car driven.