3
INTRODUCTION AND OBJECTIVES
Laboratory investigations involve taking measurements of
physical quantities, and the process of taking any measure-
ment always involves some experimental uncertainty or
error.* Suppose you and another person independently took
several measurements of the length of an object. It is highly
unlikely that you both would come up with exactly the same
results. Or you may be experimentally verifying the value of
a known quantity and want to express uncertainty, perhaps
on a graph. Therefore, questions such as the following arise:
Whose data are better, or how does one express •
the degree of uncertainty or error in experimental
measurements?
How do you compare your experimental result with •
an accepted value?
How does one graphically analyze and report •
experimental data?
In this introductory study experiment, types of experi-
mental uncertainties will be examined, along with some
methods of error and data analysis that may be used in
subsequent experiments.
After performing the experiment and analyzing the
data, you should be able to do the following:
1. Categorize the types of experimental uncertainty
(error), and explain how they may be reduced.
2. Distinguish between measurement accuracy and pre-
cision, and understand how they may be improved
experimentally.
3. Defi ne the term least count and explain the meaning
and importance of significant figures (or digits) in
reporting measurement values.
4. Express experimental results and uncertainty in appro-
priate numerical values so that someone reading your
report will have an estimate of the reliability of the
data.
5. Represent measurement data in graphical form so as to
illustrate experimental data and uncertainty visually.
EXPERIMENT 1
Experimental Uncertainty (Error)
and Data Analysis
EQUIPMENT NEEDED
Rod or other linear object less than 1 m in length•
Four meter-long measuring sticks with calibrations •
of meter, decimeter, centimeter, and millimeter,
respectively
†
Pencil and ruler•
Hand calculator•
3 sheets of Cartesian graph paper•
French curve (optional)•
*Although experimental uncertainty is more descriptive, the term error
is commonly used synonymously.
THEORY
A. Types of Experimental Uncertainty
Experimental uncertainty (error) generally can be
classifi ed as being of two types: (1) random or statistical
error and (2) systematic error. These are also referred to as
(1) indeterminate error and (2) determinate error, respec-
tively. Let’s take a closer look at each type of experimental
uncertainty.
R (I) S E
Random errors result from unknown and unpredictable
variations that arise in all experimental measurement situa-
tions. The term indeterminate refers to the fact that there is
no way to determine the magnitude or sign (+, too large; –,
too small) of the error in any individual measurement.
Conditions in which random errors can result include:
1. Unpredictable fluctuations in temperature or line
voltage.
2. Mechanical vibrations of an experimental setup.
3. Unbiased estimates of measurement readings by the
observer.
Repeated measurements with random errors give slightly
different values each time. The effect of random errors
may be reduced and minimized by improving and refi ning
experimental techniques.
S (D) E
Systematic errors are associated with particular measure-
ment instruments or techniques, such as an improperly
calibrated instrument or bias on the part of the observer.
The term systematic implies that the same magnitude
and sign of experimental uncertainty are obtained when
†
A 4-sided meter stick with calibrations on each side is commercially
available from PASCO Scientifi c.
