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Homework 1 Due March 10,2005 In 1798 the English scientist Henry Cavendish measured the density of the earth by careful work with a torsion balance. The variable recorded was the density of the earth as a multiple of the density of water. Here are Cavendish’s 29 measurements 5.50 5.61 4.88 5.07 5.26 5.55 5.36 5.29 5.58 5.65 5.57 5.53 5.62 5.29 5.44 5.34 5.79 5.10 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.30 5.75 5.68 5.85 A. Make a stem and leaf display. 48 8 49 50 7 51 0 52 9 6 9 7 53 4 4 0 6 9 54 2 7 4 6 55 0 7 3 5 8 56 1 2 3 8 5 57 9 5 58 5 B. Do a five number summary. 5.46 5.61 5.30 5.85 4.88 C. Determine whether there are any outliers. . IQR = 5.61 – 5.30 = .31 4.88 is an outlier C. Make a boxplot. . . 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 D. Use your calculator to obtain the sample mean and sample standard deviation. x = 5.4479 s = .22095 E. Comment on the shape of the distribution. Is it symmetric skewed normally distributed. The distribution is skewed toward the lower values. Otherwise it is normally distributed. F. According to Chebychev rule at least 3/4 of the data points should be within two standard deviations of the mean and at least 8/9 of the data points should be within three standard deviations. If the data were normally distributed the empirical rule says that about 2/3 of the data points would be within one standard deviation and about 95% of the data points should be within two standard deviations. For this data what percentage of the data points are within one two or three standard deviations of the mean. Does the data behave like Chebychev’s rule says it should? Does the data appear to come from a normal population based on the empirical rule? One sd (5.23, 5.67) 22 of the 29 values are within one sd Two sd (5.01,5.89) 28 of the 29 values are within 2 sd Three sd (4.79, 6.11) all of the values are within three sd The data does appear to behave like Chebychev inequality says it should since more than 75% of the values are within two sd and more than 89% of the values are within three sd. About 76% of the values are within one sd more than 69% the normal curve would predict and more than 95% of the values are within two sd so there may be a deviation from normality.