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The Penny Experiment Revisited: An Illustration of Significant Figures, Accuracy, Precision, and Data Analysis

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Joseph Bularzik

Department of Chemistry and Physics, Purdue University Calumet, Hammond, IN 46323-2094

J. Chem. Educ., 2007, 84 (9), p 1456

DOI: 10.1021/ed084p1456

Publication Date (Web): September 1, 2007

Abstract

Measuring the mass of many pennies has been used as an easy way to generate data for exercises with statistical analysis. In this general chemistry laboratory the densities of pennies are measured by weighting the pennies and using two different methods to measure the volumes. There is much to be discovered by the students on the variability of the values measured by these simple techniques. The average and standard deviation calculated for the densities measured by the different methods demonstrate that one measurement method is more accurate while the other method is more precise. Some of the measurement techniques yield density values precise enough to separate the densities of old pennies from new pennies. Some of the techniques have too large of an inherent error. Also for this simple process the bias of the numbers caused by the way the students measure the pennies is dramatically demonstrated. The data collected from this procedure can be used for a more advanced analysis and used in advanced courses, such as physical chemistry. The generated data does not give a Gaussian distribution, and the reasons for this asymmetry can be explained. An ANOVA analysis can illustrate which students have similar techniques and which ones are statistically different.