the student’s hands. The data should be recorded to 0.01s. Student must try to keep the
amplitude of the pendulum swing consistent, even if it means restarting. Next the
students will use all of the data to compute the mean value of the period and the standard
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View Full Documentdeviation of the mean., using the formulas x=
Σ
n
i=1
x
i
/N
where N=number of trials and
σ=sqrt(Σ
n
i=1
(x
i
x)
2
/N).
Next the students must plot a histogram. In order for a student to
do that, they will need a “bin” number. To get that they will divide the range of measured
values into ten intervals otherwise known as bins. Firstly divide the range of
measurement by 10((data point maxdata point min)/10). Next the students must figure
out the last column of data with the analytical formula for the normal distribution, which
is only valid for large number of measurements, n=N
0
exp{(tT)
2
/2σ2), where t is the
mean value and N
0
corresponds to the peak of the distribution curve, which occurs at
t=t.
Then plot this function on the same graph to observe how well their measurements
approximate the ideal distribution. After plugging in all the formulas and graphing the
two histograms on the same scatterplot our curve is not exactly “normal” but it is pretty
close to a bellshaped curve, which is considered “normal.”
Unfamiliar Terms
:
Standard Deviation
:
a measure of dispersion in a frequency distribution, equal to the square
root of the mea of the squares of the deviations from the arithmetic mean of the distribution.
(dictionary.com)
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 Fall '11
 BrunoBauer
 Physics, Normal Distribution, Standard Deviation, Tom Rushton

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