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Physics 207 Pre-lab — Density of Water/Standard Deviation and Error Analysis
Name____________________________________________
Date________
Grade________
Instructions: Note that this is a pre-lab for the Density of Water lab. Answer the questions
below in preparation for the lab experiment. This pre-lab must be handed in at the start of the
actual lab meeting in order to conduct the experiment. Pre-labs won’t be accepted once the lab
experiment is started. Only legible answers will be considered for grading.
All measurements are subject to errors, and the purpose of today’s simple experiment is to calculate the
uncertainty of the experimentally obtained value for the density of water, and the percentage error of the
experimentally obtained density compared to the known value. The sources of error in the experiment
can be broadly divided into three categories: random errors, systematic errors, and personal errors due
to the mistakes made by the experimenter. The third category is fundamentally different from the first two
– mistakes can always be eliminated if the person performing the experiment is sufficiently careful, and
there are even ways to distinguish them from other (unavoidable) uncertainties if the experiment is
conducted with care. Systematic and random errors, however, are intrinsic to the measurement process
and cannot be completely eliminated. Systematic errors are errors that tend to be in the same direction
for repeated measurements, yielding the value that is either consistently above or consistently below the
true value of the quantity being measured.
Systematic errors are an indicative measure of the accuracy of the experiment (the deviation of the
measured value from the true value). They are often a result of a flaw in the experimental apparatus (for
example, incorrectly calibrated voltmeter for measuring voltage, or a ruler that has been stretched or
shrunk for measuring length) or failure to take into account factors that have a significant influence on the
outcome of the experiment (for example, friction or air resistance). The concern with systematic errors in
the laboratory experiments is usually twofold – to attempt to eliminate any obvious systematic errors to
the extent possible, and to attempt to identify any data that show systematic error and suggest possible
causes for the error.
Random errors are due to the unpredictable and unknown variations in the experimental process, and
manifest themselves as a variation in the result of the measurement when the measurements is repeated
multiple times, even if the experiment is conducted as carefully as possible each time. Multiple trials for
measuring the same experimental parameter are often necessary to improve the accuracy and the
precision of the obtained experimental value. The result of n repeated measurements can be reported
as a mean value (arithmetic mean, x ), which is the best approximation of the true value, and the range
defined by the standard error,
x=x±
MG’15 / NZ ’21, ‘22
Page
In this lab, you will measure the mass and the volume of water several times in order to determine the
density of water, and compare the obtained value to the known value for the density of water by
calculating the percentage error. You will also quantify the random error by finding the standard deviation
and the standard error of the series of experiments.
1
The detailed procedure for determining the mean value, the standard deviation and the standard error is
described on the next page.
2
Page
MG’15 / NZ ’21, ‘22
Given the following collected data (all measured in seconds):
59.9, 65.1, 61.3, 62.2, 53.7, 55.5, 60.1, 70.0, 64.1, 56.3, 58.3, 58.2, 62.1, 62.4, 68.6, 65.8,
56.4, 59.3, 68.2, 61.0, 67.1, 59.8, 65.2, 61.1, 62.1, 53.9, 55.6, 60.2, 68.2, 64.3, 56.7, 58.8,
58.7, 62.3, 62.2, 63.1
Calculate σn-1
Show all your work
σn-1= ____________________
Page
3
What conclusions do you draw from the above answer?
MG’15 / NZ ’21, ‘22
Calculate α
Show all your work
α = ____________________
What conclusions do you draw from the above answer?
Page
4
What conclusions do you draw from the data set?
MG’15 / NZ ’21, ‘22
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