1
Uncertainty
UNC
Uncertainty
revised October 18, 2004
Learning Objectives:
During this lab, you will learn how to
1.
estimate the uncertainty in a directly
measured quantity.
2.
estimate the uncertainty in a quantity
that is calculated from quantities that
are uncertain.
3.
use
Origin
to perform calculations,
make graphs, and perform linear
regression.
4.
look at a graph with data and a model
and determine if the data support the
model.
(
You will turn in two worksheets and
two graphs for this lab. The worksheets
(UNC Worksheet and Error Analysis and
Propagation Exercise) are included in
Appendix IX of the lab manual. The material
for this lab is due one week from the date of
your lab at 6:00 PM.
)
A. Introduction
The purpose of this laboratory is to
accustom you to recording measurements.
You will measure mass, time, length, and
force. Besides learning some basic measure
ment techniques, you must realize that all
measurements possess some
uncertainty
in
their values. When you make a measurement
(
x
), you must estimate the
absolute uncer
tainty
(
δ
x
) in your measurement. This quan
tity is based upon how well you think that
you could make the measurement. The abso
lute uncertainty may be a function of the
quality of the measuring instrument, the
nature of the quantity being measured, the
ability of the individual making the meas
urement, and the conditions under which the
measurement is made. Too often we assume
that the absolute uncertainty is based solely
on the
resolution
of the measuring instru
ment. The resolution is the smallest gradua
tion on a scale or the last decimal place in a
digital readout. The absolute uncertainty
often depends on several of the factors
above. There is no prescribed formula of
how to calculate the absolute uncertainty for
a measured quantity. For this reason, it is
necessary for you to discuss how you
determine the absolute uncertainty of a
measurement in the Procedure paragraph of
a laboratory report. Taking the measured
value and the absolute uncertainty together,
you report the
measurement interval
(
x
±
x
). This symbol
x
±
x
represents the
interval in which we have confidence the
measured value lies. Remember to always
report the absolute uncertainty (
x
) together
with your best estimate of the measured
value (
x
).
There are
rounding rules
that guide us
in reporting the number of digits in the
answer. For example, we would not report a
number such as 2.1789345 meters if we
were really only sure of the reading to
within 0.01 meters. Instead, we would report
the value as 2.18
±
0.01 meters, i.e., we
estimate that the value lies somewhere
between 2.17 and 2.19 meters. In Physics
laboratories, we will adopt the simple rule
that
the
absolute
uncertainty
of
a
measurement is reported to only one, or at
most two, significant figure(s), and the
measurement is then rounded to the same
decimal place as its absolute uncertainty.
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 Spring '08
 kernan
 Double click, absolute uncertainty, Dr. L. M. Krauss

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