Unit 2 Assignment Part A For the following set of data, determine the mean, median, mode, standard deviation, and IQR. Create a box & Whisker plot. Show all work. 12, 45, 35, 76, 85, 23, 92, 76, 68 Part B Justin is a Grade 12 student planning to go to university next year. He has studied hard and is proud of his overall average of 82%. However, Justin is uncertain of where he stands in relation to other classmates applying to university. By using his understanding of statistics, Justin hopes to determine his chances of being accepted into the university of his choice. Below is a list of the average marks of all the Grade 12 students in Justin's school who are applying to university: 75 72 76 63 53 48 81 78 67 63 76 78 55 3787 90 74 1820 64 66 70 82 64 79 71 75 71 73 678 87 77 75 70 59 75 69 85 1863 76 78 72 22 72 63 54 1. Determine the mean average, median and mode of the students. 2. Based on these results verify including the definition, whether the distribution is a normal distribution, right-skewed, or left-skewed. 3. In order to make some valid comparisons, Justin needs to know the spread of data in his school. Determine the standard deviation of the group to the nearest hundredth. (technology would be best!) 4. Calculate the upper and lower quartile values Q3 and Q1 as well as the IQR. 5. In which quartile of the group does Justin's average mark of 82% fit? 6. How many Grade 12 students in Justin's school have an average within one standard deviation of the mean? Within two? Within three? Be sure to show all your calculations! 7. Based on your answer to #6 is this a normal distribution? How does this agree or disagree with your answer to #2? 8. State the definition and significance of a z-score. 9. Calculate the z-score for Justin's average mark. Based on this result, use the table on page 398 to determine the percent of the class that has a lower average mark than Justin. 10. Is this true? Why or why not? [Hint: how many students have lower marks than Justin out of the total students?] 11. What would Justin have to raise his average mark to if he wants to be in the 90th percentile? 12. Many universities use weighted averages to calculate Grade Point Average (GPA) for students. Use the chart on Page 196 of your textbook to calculate Justin's GPA for the following courses and weights: English 86 1 credit Advanced Functions 83 2 credits Geometry and Vectors 78 1 credit Data Management 88 1.5 credits History 74 1 credit Physics 77 1 credit Civics 92 0.5 credit If you are unsure of how to do this research Grade Point Averages on the internet. You should become familiar with the method you will be evaluated with at university or college.