hw5_solution_2008

hw5_solution_2008 - ME 17, APPLIED NUMERICAL METHODS...

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ME 17, APPLIED NUMERICAL METHODS SOLUTION HOMEWORK 5 TA: GAURAV SONI Problem1: Part A: The data set for this problem represents final scores of ME151C class from Spring 2008. The matlab code is attached for finding the mean, the median and the standard deviation. Following are the answers: Mean = 75.2994 Median = 76.0566 Standard Deviation = 8.0199 Part B: The mean score was subtracted from the data. The histograms of this data were created using different numbers of bin. Following figures show these histograms. When number of bins is only 2, the histogram does not reveal much information about the shape of the data distribution. For higher number of bin (5 and 10), the histogram shows a smooth shape of the distribution. For very high number of bins (i.e. 20), the discreteness of the data is revealed. In other words, some of the bins remain completely empty. Histogram with 2 bins -25 -20 -15 -10 -5 0 5 10 15 20 0 10 20 30 40 50 60 70 xd frequency
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Histogram with 5 bins -25 -20 -15 -10 -5 0 5 10 15 20 0 5 10 15 20 25 30 35 40 xd frequency Histogram with 10 bins -25 -20 -15 -10 -5 0 5 10 15 20 0 2 4 6 8 10 12 14 16 18 20
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Histogram with 20 bins -25 -20 -15 -10 -5 0 5 10 15 20 0 2 4 6 8 10 12 14 xd frequency PART C The skewness of the data x is given by where μ is the mean of x , σ is the standard deviation of x , and E ( t ) represents the expected value of the quantity t . For discrete data sets, the skewness can be written as For the class scores, I obtained a skewness value of -0.5262. Students might also get - 0.5351 depending on which skewness function they used (mine or Matlab’s). Both values will get full points. A negative value of skewness signifies that the left tail of the distribution has more data. In other words, the data is more spread out towards the left. This behavior can be seen in the histograms printed above. One can note that our histograms are more spread out towards the left tail of the histogram. Following is a figure from wikipedia, explaining the skewness of a distribution
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PART D The bell shape of the histogram suggests that the data is similar to a normal distribution.
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hw5_solution_2008 - ME 17, APPLIED NUMERICAL METHODS...

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