STAT:101O Statistics and Society Instructor: Max Sampson HOMEWORK 4 Answer the questions neatly and in order. Use complete sentences where appropriate. Show all work andror computations. Charts and graphs should be done by hand and roughly to scale. Submit your work as a single pdf file to CanvasflCON. Problem #1 The table below gives information about students\" scores from the final exam in a history course. Note: \"up to X\" means values below x but not including values equal to x Scores I Cumulative Frequency 50 up to 60 4 60 up to 70 12 70 up to 80 ' 35 80 up to 90 ' 65 90 up to 100 80 a) What is the total number of students who took the exam? b) What proportion of students scored \"50 up to 60"? c) How many students scored \"60 up to 70\"? d) What proportion of students scored less than 80? e) How many of the students scored at least 70 but less than 90? Problem #2 Max created the following pie chart to visualize how his students get to campus. Bike Bus Drive STAT:1010 Statistics and Society Instructor: Max Sampson a) What, if anything, is missing from the pie chart? b) What is the most common way Max's students get to campus? 0) What is the least common way Max's students get to campus? d) Do you think this is the best visualization to use? Why or why not? Problem #3 The distribution of geographic home for students at the University of Iowa in the fall semesters of1985 and 2015 are shown below. (source: htt :fiiruiowaedufre istrar rotilesi) Geographic Home Origin Frequency Frequency 1985 2015 _ lowa . States Adjoining Iowa 100 I 80 60 I Other States 8 U.S.Territories D . Foreign Countries 1,662 V Total 29,651 32,150 Percent 20 1985 2015 a) Identify the type of graph that is shown. Do you think it is easy to compare the data from 1985 to the data from 2015? Why or why not. b) This graph does not have a legend. What do each of the colors represent? Explain your reasoning. c) What does the graph tell you about students enrolled at the University who are from the state of Iowa? CARE about your answer. (I) What is the percent change in the number of students from foreign countries from 1985 to 2015? e) What is the change in the percentage of students from foreign countries from 1985 to 2015? f) Based on the graph, do you think the enrollment of students at the University of Iowa in 2015 was more or less diverse than in 1985? Explain your reasoning. g) Here is a graph from the actual 2015 report. Explain why this graph is misleading. C'TiT-dn'tn Unmn..rnrlr-HJI '3 STAT: 1010 Statistics and Society Instructor: Max Sampson 17,531 18,000 16,000 14,000 2,000 7.133 10,000 8,000- 4,120 3,336 6,000 4,000 30 2,000 lowa States Other U.S. Foreign Adjoining States Territories Countries lowa Problem #4 The following histogram indicates the relative frequencies of ages of U.S. scientists in 1967. + 20 25 30 35 40 45 50 55 60 65 70 75 a) What is missing from this graph? That is, if a student submitted this graph, why would they lose points? b) At what age would you estimate the median? The median is the point where a vertical line divides the histogram into equal areas, 50% on each side. Just give an estimate; something close. If this takes you more than 2 minutes you are thinking too much. c) What bin width was used to construct this histogram? Explain your reasoning. d) Approximately what percentage of scientists in 1967 were between 25 and 40 years of age? Round your answer to the nearest 10%. e) What might explain the big "jump" at age 25