Assignment - Introduction to Statistics Course Incharge: Rabia Shakir Q#1. Given the random sample, x 1, x 2, …… . x η. Show that ∑i=1^n(xi-ẋ)=0 Q#2. The numbers of goals scored by a college lacrosse team for a given season are 4,9,0,1,3,24, 12,3,30,12,7 (2024)

Assignment - Introduction to StatisticsCourse Incharge: Rabia ShakirQ\#1. Given the random sample, \( x 1, x 2, \ldots \ldots . x \eta \). Show that \( \sum_{i=1}^{n}\left(\mathrm{x}_{i}-\dot{\mathrm{x}}\right)=0 \)Q\#2. The numbers of goals scored by a college lacrosse team for a given season are \( 4,9,0,1,3,24 \), \( 12,3,30,12,7,13,18,4,5 \), and 15. Treating the data as a population, calculate the mean and standard deviation.Q\#3. The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:\begin{tabular}{llll}3.2 & 1.9 & 2.7 & 2.4 \\2.8 & 2.9 & 3.8 & 3.0 \\2.5 & 3.3 & 1.8 & 2.5 \\3.7 & 2.8 & 2.0 & 3.2 \\2.3 & 2.1 & 2.5 & 1.9\end{tabular}Calculate the mean and standard deviation.Q\#4. A taxi company tested a random sample of 10 steel-belted radial tires of a certain brand and recorded the following tread wear \( 48,000,53,000,45,000,61,000,59,000,56,000,63,000 \), \( 49,000,53,000 \), and 54,000 kilometers. Find the standard deviation of this set of data by first dividing each observation by 1000 and then subtracting 55 .Q\#5. Mean deviation: the mean deviation of a sample of \( \mathrm{n} \) observation is defined to be \( \sum_{i=1}^{n} \quad\left|\mathrm{x}_{i}-\dot{\mathrm{x}}\right| / \mathrm{n} \). find the mean deviation of the sample \( 2,3,5,7 \), and 8 .Q\#6. The Apollo space program lasted from 1967 till 1972 and included 13 missions. The missions lasted from as little as 7 hours to as long as 301 hours. The duration of each flight is listed below.\begin{tabular}{|ccccc|}\hline 9 & 10 & 195 & 295 & 241 \\142 & 301 & 216 & 260 & 7 \\244 & 192 & 147 & & \\\hline\end{tabular}a. Explain why the flight times are population?b. Verify that \( \Sigma(X-X)=0 \)Q\#7. The following data represent the length of life in minutes, measured to the nearest tenth, of a random sample of 50 black flies subjected to a new spray in a controlled laboratory experiment:\begin{tabular}{|c|c|c|c|c|}\hline 2.4 & 0.7 & 3.9 & 2.8 & 1.3 \\\hline 1.6 & 2.9 & 2.6 & 3.7 & 2.1 \\\hline 3.2 & 3.5 & 1.8 & 3.1 & 0.3 \\\hline 4.6 & 0.9 & 3.4 & 2.3 & 2.5 \\\hline 0.4 & 2.1 & 2.3 & 1.5 & 4.3 \\\hline 1.8 & 2.4 & 1.3 & 2.6 & 1.8 \\\hline 2.7 & 0.4 & 2.8 & 3.5 & 1.4 \\\hline 1.7 & 3.9 & 1.1 & 5.9 & 2 \\\hline 5.3 & 6.3 & 0.2 & 2 & 1.9 \\\hline 1.2 & 2.5 & 2.1 & 1.2 & 1.7 \\\hline\end{tabular}Using 8 intervals with the lowest starting at 0.1 ,a) Set up frequency distribution.b) Construct a cumulative distribution.

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