lab1 - curves the number of trails needs to be large. The...

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SAMPLE CALCULATIONS -Calculation of average x position, x av , for 300 marble rolls: x av = Σ n(x) * x = 1 (-10) + 2 (-9) + …… = 0.957 ________ ________________ N 300 -Calculataion of sigma for 300 marble rolls using the method of the lab manual: 1) Σ n(x) * (x - x av )^2 = 1 (-10 – 0.957)^2 + (-9 – 0.957)^2 + …… = 4720.4367 2) σ^2 = [Σ n(x) * (x - x av )^2]/ (N-1) = 4720.4367/300 3) σ^2 = 15.734789 4) σ = 3.966710098 5) round it to σ = 3.97 -Calculation of the Gaussian distribution using σ = 3.97, and x av = 0.957: The Gaussian equation is: G(x) =
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CONCLUSION In this lab we used the Gaussian probability distribution equation to describe the path of a marble rolled down a board of nails, and found that this distribution adequately described the data collected from the experiment. The Gaussian distribution adequately approximated the histogram obtained using 300 marble rolls. The histogram drawn using the data from 50 marble rolls does not resemble the Gaussian curve because it does not have an adequate number of trails. In order to describe something using statistical
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Unformatted text preview: curves the number of trails needs to be large. The 300 marble rolls data resembled the Gaussian curve, whereas the 50 marble rolls data did not. So, as the number of data points increases, the histogram becomes closer to the Gaussian curve. Furthermore, the size and shape of the marble used to roll down the board of nails changes the results of the experiment. Using a marble with a smaller radius increases the value of sigma. The smaller marble will roll faster and thus hit fewer nails, and therefore, follow a more straight path. In analyzing the data, possible errors can be detected. The value obtained for x av in all cases was not 0. Zero is the correct average for a marble whose path is completely random. This error can be fixed if more samples for the data is taken. It could also be because the board which the marbles were rolled down was not level to the ground....
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lab1 - curves the number of trails needs to be large. The...

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