Overview: This exercise serves as an introduction to histograms. Students are given a short introduction to histograms in lecture and reading. They are then broken up into different groups of 3-5 students. Students start by making a prediction about the distribution of the weights of the pennies they have been given. Each group then weighs their pennies and: 1) enter their data into a spreadsheet of results for the entire class and 2) each student must draw a histogram of their own results. Each group must then interpret their graphs and each student must explain in writing how their graphs either confirms or disproves their initial predictions. While students are working, the instructor creates a histogram of the data from the entire class. After students have completed the written part of the assignment, each group gives a short summary of their predictions, their results, and their conclusions.
Results: The students find that 2 sets of pennies have overlapping weights (mean = 2.5 g, stdev = 0.2 g), while the third set is slightly different (mean 3.1 g, stdev = 0.2 g). The instructor can then lead a discussion around the topic of variability and how to statistically evaluate whether or not different data sets are statistically similar. This discussion should include how to account for instrumental error. This leads into a discussion of the meaning of mean values and standard deviation. This discussion can also include a comparison of how the results from an individual group compares with the data set from the whole class: this serves as a good place to discuss how scientists determine how much data to collect for a given project. This and similar exercises are thus needed before students start to interpret their own data. Expected Outcomes: Students will gain an understanding of how to read a histogram and how to evaluate the meaning of mean values and standard deviations.