Homework 7
Math 114Q, Section 10

Due in class Tuesday, October 30.

  1. There is one assigned text for this course. It is Darrell Huff's How to Lie With Statistics . If you have not bought a copy of it yet, please do so by October 30.

  2. The UMass Boston Office of Institutional Research collects and analyzes data about the university. Each year they publish a Statistical Portrait of the University every year; most of this information is available online. You can find the 2006 statistical portrait at www.oirp.umb.edu/2006/stat_portrait/index.html. Go there and scroll down to Table 30: Undergraduate Major Enrollment by Gender and Ethnicity. Download this table as an Excel file.

    1. Open a new spreadsheet and set up three columns with the following headings: College; Number of Men; Number of Women. Cut and paste information from Table 30 to fill in the table in the new spreadsheet. Your finished spreadsheet should show the total number of men and women (use the unduplicated head count) in each college. Put your name on the spreadsheet, include the source of the data, and save it.

    2. Use Excel to make a double bar chart with the information on your new spreadsheet. Label the chart carefully. Remember to include your name, the date, and the data source.

      If necessary, change colors and patterns so that the chart is legible when printed in black and white.

    3. Go back to your original table. Use Excel to find the total enrollment in each college, then find the percentage of men and the percentage of women in each college. Make a double bar chart showing these percentages. Again, label it appropriately.

    4. Print the new table (showing the percentages) and your two charts. Use them to write a brief analysis of the distribution of undergraduate enrollment at UMass Boston. You may want to comment on the total number of students in each college or the distribution of men and women among the colleges. Make sure you include relevant data in your discussion and that the data you cite support your main points. Type this, proofread it, revise it, etc. and print it to be turned in with this assignment.

    5. What does "unduplicated head count" mean? Why would Institutional Research record enrollments this way?

  3. Go to the website www.census.gov/ipc/www/idb/pyramids.html. You can use the options on this site to create a population distribution graph called a population pyramid. First construct a population pyramid for the United States for the year 2006. Print your pyramid. Go back to the beginning page and select the Sudan. Construct a population pyramid for the Sudan for the year 2006 and print the graph.

    1. Use your graph to estimate the number of people in the United States who were between 0 and 9 years old in 2006. Do the same for the Sudan. You can click on the "Extract data from IDB Online Aggregation" button to get a more accurate answer, but an estimate is fine here and in the rest of the problems. (You will see that the web page that shows the raw data used to build the pyramid is just plain text. That's a nuisance if you want to put the numbers into a spreadsheet in order to study them further. You should be given the option of downloading the data in Excel format.)

    2. In the United States, which age interval is the largest (group men and women together)? What about in the Sudan?

    3. In the United States, which age interval is the smallest (group men and women together). What about in the Sudan?

    4. Make two quantitative observations about the age distribution of population in the United States in 2006.

    5. Make two quantitative observations about the age distribution of population in the Sudan in 2006.

    6. Compare the age distributions of the populations in these two countries.

  4. Download the spreadsheet RedSoxSalaries.xls. There you will find player salaries for the 2007 Boston Red Sox.

    1. Sort the table so that the salary column is in ascending order.

    2. According to data on the espn.com website, the mean salary for all major league baseball players in 2007 was $3,127,946 while the median player salary was $1,050,000. Write a couple of sentences comparing the Red Sox mean and median salaries to the league mean and median salaries. (Since the data is sorted by salary it's easy to find the Red Sox median. Use Excel to compute the mean.)

    3. Create salary intervals that are $99,000 wide. The first interval will be $300K to $399K, the next $400K to $499K, and so on. Use the sorted salary column to count the number of players in each salary interval. http://www.oirp.umb.edu/ Use two new columns of the spreadsheet to construct a table showing the salary intervals and the number of players in each. Label the columns clearly.

    4. Make a histogram using the data in your salary interval table. Push the bars together, label the chart and make sure the colors and patterns are appropriate for black and white printing, as we did in class. Arrange the chart and the two tables (four columns of data) so that everything is visible on one page when you print the spreadsheet. Use the data provided to finish this problem.

    5. In fall 2002, USA TODAY published Baseball salaries top-heavy by Tom Weir and MaryJo Sylwester. (If you wish you can read the whole article at asp.usatoday.com/sports/baseball/salaries/2002-10-16-analysis_x.htm ). In the article, the authors write
      A few players with big salaries are grabbing an ever-increasing share of the payroll, pushing more players toward the low end of the scale. That means baseball's middle class - the journeymen, midlevel players and rising stars who make up the 60% of players in the center of the payroll - are taking home less of the payroll pie each year.

      This season [2002] they accounted for 35% of the total dollars paid out. In 1988 they made 41% of the money.

      One of baseball's biggest salary trends mirrors that of the American worker: a shrinking middle class...

      Calculate the percentage of the Red Sox current payroll earned by players in the two highest salary intervals. Then calculate the percentage of the Red Sox payroll earned by players with salaries less than the team median. Do these statistics support or contradict the trend reported in the USA TODAY article? Explain your answer.

  5. The following (made up) table shows the salary structure of two departments in a hypothetical university.
    
     	Physics				English
     	# in dept	salary		# in dept	salary
     Women	1		$100K		9		$50K
     Men	9		$90K		1		$40K
     

    1. What is the average (mean) salary of the women professors? Of the men?

    2. What is the average (median) salary of the women professors? Of the men?

    3. What is the average (modal) salary of the women professors? Of the men?

    4. Write a few sentences to convince someone that men in this university are paid better than women. Then write a few sentences to convince someone of just the opposite. Can you explain the contradiction?