1.10, 1.11, 1.12, 1.13 and 1.14 please

1.10 Consider the following data: ONS AND PROBLEMS OF TOPIC I 86 144 81 72 103 132 97 108 110 107 80 87 106 91 118 110 96 82 84 92 99 110 98 86 117 120 70 125 87 104 83 57 85 46 92 83 1 10 66 148 80 92 109 86 95 92 110 89 118 83 102 107 70 99 94 104 130 88 88 108 75 163 91 89 131 98 108 97 87 97 107 76 94 117 151 89 80 134 100 104 92 74 115 108 106 103 96 65 91 100 87 123 97 86 84 106 110 102 96 94 161 (a) Form a frequency table and plot a frequency distribution of this data. (b) Calculate the mean value of the data. (c) Find the equation for the normal distribution that would fit the data as closely as possible. (d) Plot the normal distribution curve that is described by this equation. 1.11 Tabulate the relative frequencies for the following data and represent them graphically. X 15 16 17 18 19 20 21 22 23 24 1 4 7 12 13 9 6 4 3 1.12 Find the standard deviation of the following set of measurements: 15, 21, 19, 20, 18, 17, 22, 23, 16, 25. 1.13 Find the standard deviation of the set of measurements that occur with the frequencies tabulated below: 1 2 13 4 5 6 7 8 9 10 15 21 19 20 18 17 22 23 16 25 X 11 12 14 9 6 19 5 3 1.14 (a) Calculate the standard deviation o of the distribution consisting of the integers 1 to 5 inclusive. (b) Samples are taken of these integers, with each sample consisting of three different integers (10 samples in all) and a second distribution is formed from the means of these samples. If s is the standard deviation of this second distribution, prove that So = 1V6