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