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.
Introduce high school students to the art and science of statistics in the 6-minute video, "What is Statistics?" from the Against All Odds series. This video resource will demonstrate how gathering, organizing, drawing, and analyzing data is applicable in everyday life and a variety of careers.
Discover how calculating median and mean reveal different ways to describe a center of distribution in this 9-minute video from the Against All Odds statistics series. This video resource will examine differences in comparable wages for men and women to see practical applications of statistics and data visualization.
This exercise was developed to complement the film The National Parks of Texas by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.
This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.
Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page.
This topic introduces students to the idea of using a smooth curve to model a data distribution, eventually leading to using the normal distribution to model data distributions that are bell-shaped and symmetric. Many naturally occurring variables, such as arm span, weight, reaction times, and standardized test scores, have distributions that are well described by a normal curve. Students begin by reviewing their previous work with shape, center, and variability. Students use the mean and standard deviation to describe center and variability for a data distribution that is approximately symmetric. This provides a foundation for selecting an appropriate normal distribution to model a given data distribution. Students learn to draw a smooth curve that could be used to model a given data distribution. A smooth curve is first used to model a relative frequency histogram, which shows that the area under the curve represents the approximate proportion of data falling in a given interval. Properties of the normal distribution are introduced by asking students to distinguish between reasonable and unreasonable data distributions for using a normal distribution model. Students use tables and technology to calculate normal probabilities. They work with graphing calculators, tables of normal curve areas, and spreadsheets to calculate probabilities in the examples and exercises provided (S-ID.A.4).
Note: Although this module is identified as Algebra II in the EngageNY curriculum, it corresponds to the Precalculus Alabama Course of Study.