Physics
Electricity measuring equipments Solutions
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Par Lab 1 Error Analysis pdf
Axav=o/VN
Uncertainty
In the Mean
(Axml
Uncertainty in the mean value of x.
The actual value of x will be
somewhere in a neighborhood
around. This neighborhood of
values is the uncertainty of the mean.
X = X AX vg
Measured Value
The final reported value of a
measurement of x contains both the
average value and the uncertainty in
the mean
Most of the time we will be using the formulae for small data sets. However, occasionally we
perform experiments with enough data to compute a meaningful standard deviation. In those
cases we can take advantage of software that has programmed algorithms for computing Xavg
and o
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Experimental Data:
The following data were taken for a pendulum with a length of 121 + 1cm. The data
in the left column were measurements of individual periods. The data in the right
column were for the time it took for 10 oscillations of the pendulum.
Period (s)
1.98
2.22
2.00
2.13
2.16
2.15
2.10
2.28
2.41
2.19
Ten Periods (s)
21.92
22.38
22.11
22.00
21.89
Use the appropriate error analysis method and determine the mean, the uncertainty in the
mean and the uncertainty in the measurements for each set of data. Given that the period of
a simple pendulum is given by:
T = 27V(L/g)
Where L is the length of the pendulum and g is the acceleration due to gravity, determine
which method provides the best precision and which the best accuracy. The same set may
do both.
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