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The data set shows the January 1 noon temperatures in degrees Fahrenheit for a particular city in each of the past 6 years. 28 34 27 42 52 15 (a) What is the five-number summary of the data set? (b) What is the mean, X, of the data set? (c) What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work. X X-X (x-x) Answer: Sum: (d) What is the standard deviation of the data set? Use the sum from Part (c) and show your work. (Score for Question 2: _ of 15 points) Math | Graded Assignment | Practical Math Semester I est, Part 2 A linear model for the data in the table is shown in the scatter plot. x Y 1 2 2 6 5 6 6 9 7 11 9 10 10 13 Variable y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 Variable x Answer: (a) Which two points should you use to find the equation of the model? Circle the points on the graph. (b) What is the slope of the linear model? Show your work. (c) What is the equation of the linear model in point-slope form? (d) What is the slope-intercept form of the equation you wrote in Part (c)? Show your work. (e) What is the equation for the least squares regression line? Round the values for a and b to three decimal places. (Hint: Use a calculator or spreadsheet program.) (Score for Question 3: of 20 points) _ The matrices show the enrollment of boys and girls on the basketball, lacrosse, and soccer teams in two towns. Town A Boys Girls Town B Boys Girls Basketball 84 76 Basketball 94 70 Lacrosse 72 88 Lacrosse 88 89 Soccer 96 100 Soccer 100 110 Answer: (a) If we let matrix A be the matrix for Town A, what is the element a21, and what does it represent? (b) If we let matrix B be the matrix for Town B, what is the address of the element that represents the number of girls enrolled in soccer in Town B? (c) What is the matrix that results when you subtract matrix A from matrix B? (d) Name the matrix you found in Part (c) matrix C. What is element C12, and what information does it tell you about the number of girls enrolled in basketball in Town B compared with Town A? (e) What is the matrix that shows the enrollment in Town A after a 25% increase in enrollment in all sports and in both genders? (Hint: Find 1.25A.)