Expressing Uncertainties of Experimental Data

Overview

The goal of this experiment is for you to learn how to express the results of your laboratory exercises.  There is error in any measurement, even the most precise and accurate ones. The proper study of errors requires a whole course or two.  While we do not aim to turn you into expert experimentalists in introductory physics courses, we do want you to know how to report a result of an experiment that reflects the possible error, or uncertainty, in it.

We will use a type of uncertainty called the sample standard deviation – or more simply, standard deviation.  The formula for it is not important at the moment.  What you need to know is that when a large number of measurements are taken, the measurements cluster around an average value, normally distributed in a bell-shaped curve.  The standard deviation tells you that approximately 2/3 of the data lie within a range between the standard deviation subtracted from the average and the standard deviation added to the average.

Because we want to focus on expressing uncertainties in this “experiment”, you will not use equipment other than a computer this time.  You will enter numbers into a worksheet that will represent experimental data.  There are two parts to the experiment.  In the first, you will learn what we mean when we say “Express your result in standard form.”   In the second, you will learn about relative uncertainties.

Most results from your laboratory work in this course should be expressed in standard form. Sometimes you will be asked for a relative uncertainty. In contrast, in lectures, summary homeworks, and exams, you will report your answers in either exact form, e.g. ½, or to three significant digits, e.g. 0.500.

Now please open the worksheet and move on to Part I (links below).
 

Today's worksheet

Part I
Part II
Worksheet
Index