APStatistics 2.01 Data Distributions Directions: Complete the assignment. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. 1. Students in three different classes took the same test. Below are histograms showing the test results. 7 6 5 4 3 2 1 0 45 50 55 65 75 80 85 90 45 50 55 60 65 70 75 80 Class A: 8 7 6 5 4 3 2 1 0 Class B: 8 7 6 5 4 3 2 1 0 45 50 55 60 65 70 75 80 Class C: a. Which distribution is symmetric? (1 point) Class B is symmetric because there is a clear line of symmetry in the graph. Both sides of the highest point are symmetric. b. Which distribution is the most skewed? (1 point) Class A is the most skewed because it has a long tail extending to the left of the graph. c. In Class C, is the mean to the left or right of the median? Why? (2 points) In Class C, the mean is to the right of the median. This is true because the graph is skewed to the right and that causes the mean to be slightly higher than the median. The median is at the point that the graph would balance if it were made of solid material. The mean of a skewed distribution is pulled farther down the tail than the median, which is not affected by skewness. d. Which class had the highest median score? (2 points) Class A because the graph is skewed to the left, causing the median to be at the point in which the graph would balance if it were made of solid material. The median of class C is about 65, the median of class B is about 65 and the median of class A is about 75. e. Which class had the highest mean score? (2 points) f. Which class had the smallest IQR? (2 points) g. Which class had the smallest difference between the mean and median? (2 points) h. Which class had the smallest standard deviation? (2 points) i. Match the boxplots with the correct class histogram write a complete sentence explaining why the graphs match (6 points): j. Boxplot 1: Bo Boxplot 2: Bos Boxplt Boxplot 3: Ans 2. An AP Statistics teacher has decided to open his own tutoring business, hiring some of his students as employees. The teacher has 5 tutors, each earning $15,000 annually, a receptionist earning $11,000 annually, a pet chameleon as a mascot earning $35,000 annually, and, as CEO, the teacher earns $75,000 annually. a. Graphically determine if this data is skewed by creating a boxplot. (2 points) b. Based on the shape of your graph, is where is the mean relative to the median? (2 points) c. Describe the shape, center, and spread of this data and identify any outliers. (6 points). d. Calculate the five number summary for the distribution of salaries (2 points). e. Explain how the Q1 and median can be the same in the distribution. (4 points)