# Examples

Initial Publication Date: October 13, 2006

- Body Measures: Exploring Distributions and Graphs Using Cooperative Learning: Using cooperative learning methods, this lesson introduces distributions for univariate data, emphasizing how distributions help us visualize central tendencies and variability. Students collect real data on head circumference and hand span, then describe the distributions in terms of shape, center, and spread. The lesson moves from informal to more technically appropriate descriptions of distributions.
- Histogram Sorting Using Cooperative Learning: Using cooperative learning methods, this activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), and that not all histograms are easy to classify. Students also learn that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).
- Understanding the standard deviation: What makes it larger or smaller?: Using cooperative learning methods, this activity helps students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. This lesson also helps students to discover that the standard deviation is a measure of the density of values about the mean of a distribution. As such, students become more aware of how clusters, gaps, and extreme values affect the standard deviation.
- Investigating the Modernity of the University Library: Students work in groups to estimate the number of "new" books in the university library given a "budget" for data collection. They will first develop a sampling method, and then implement it in a pilot study. Students conduct a pilot study using a proportion of their "budget". A pilot study report is used to give students timely feedback on their design, estimation, and writing. The design or estimation strategy may be modified before completing data collection and submitting a final report.
- How well can hand size predict height?: This activity is deigned to introduce the concepts of bivariate relationships. It is one of the hands-on activities of the 'real-time online hands-on activities'. Students collect their own data, enter and retrieve the data in real time. Data are stored in the web database and are shared on the net.
- Statistics and Error Rates in Death Penalty Cases: The goal of this activity is to have students assess the quality of popular reports of an important statistical study led by Columbia University law professor James Liebman. The study examined the results of all US death-penalty cases from 1973 to 1995. Reports of the study in various newspapers and magazines produced a range of numerical summaries and graphical displays to illustrate the results, some of which were accurate while others were potentially misleading.
- Nature of the chi-square distribution: In this activity, students learn the true nature of the chi-square distribution. The distribution will be introduced via a simulation that demonstrates the fact that when a random sample of values is selected from a normal population the sum of the values will follow a Student's t-distribution, while the sum of the squares of the same values follows a chi-square distribution. Student's intuitively grasp this visual approach to describing the chi-square distribution, and it easily leads into a discussion of properties of the distribution, such as why it is always non-negative and positively skewed.