Precision and Accuracy in Measurements: A Tale of Four Graduated Cylinders

Abstract

Students need to be aware of the fact that even our best scientific measurements unavoidably involve some error. To develop this awareness, general chemistry courses introduce the concepts of precision and accuracy. The distinction between the two terms is illustrated in textbooks through the analogy of a target with arrows more or less clustered around the bull's eye. After this brief introduction many texts do not develop the subject further.This paper expands upon the topic of precision and accuracy at a level suitable for general chemistry. It serves as a bridge to the more extensive treatments in analytical chemistry texts and the advanced literature on error analysis. It presents a simple model experiment involving graduated cylinders, a discussion of some complications, and suggestions for classroom implementation. Previous articles in the Journal cover such related topics as significant figures (1-5), propagation of error (6-13), experiments and demonstrations of uncertainty (14-21), and a general review (22). Definition of TermsWe begin by defining the terms central to the theme of this paper. Measurement: the act or process of measuring. The process may be as simple as reading a thermometer or as complex as all the operations required for a chemical analysis. Precision: reproducibility. A measurement is precise if it is close to other values obtained by repeating the determination using the same procedure. Accuracy: correctness. A measurement is accurate if it is close to the true value. Since the true value of a quantity can never be exactly known, an accepted value is commonly used as the test of accuracy. Error: anything that causes a measurement to differ from the true value. The amount by which the measured value differs from the true value is also called the error.

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