You can read about averages in the (draft) Averages chapter in the updated version of Common Sense on the course web page at www.cs.umb.edu/~eb/qrbook/qrbook.pdf

Be sure to start all the problems over the weekend so that you can ask questions Tuesday about parts your stuck on.

1. A student's final grade in a Biology course is determined using the following weights:

       quizzes are worth 5%
       exam 1 is worth 20%
       exam 2 is worth 20%
       lab reports are worth 15%
       research paper is worth 15%
       final exam is worth 25%.
   

   Just before the final, a student has the following grades (all out of 100):

   	Lab report grades:  75, 90, 85, 69, 70, 75, 80, 75
   	Quiz grades:        85, 80, 0, 60, 70, 80, 80, 75
   	Exam 1:             80
   	Exam 2:             70
   	Paper:              85
   

   1. Find the student's lab report and quiz averages.

   2. What is the students course average going in to the final exam?

      Be careful. Since there's no final exam grade to include in the average, you can't just use the given percentages for the weights of the pieces that you have.

   3. The student would like have a course average of at least 83% after the final in order to earn a B. What is the lowest grade she can get on the final and achieve that goal?

      Hints. You can do this with just a tiny bit of algebra: Let x be the final grade required for a B. Set up an equation involving x and solve it. But if even that much algebra turns you off you can try guessing at the answer and then adjusting your guess until it's right.

   4. Is it possible for her to achieve a course average of 93% in order ot earn an A?

2. A student at UMB received the following grades for her first two semesters:

   Semester 1
       course      number of credits   grade
       Math 114Q       3               B+
       Soc 101         3               A-
       Eng 101         3               B
       Art 100         3               B+
   
   Semester 2
       course           number of credits   grade
       Math 125                 3               B
       First year seminar       4               C
       Eng 102                  3               B-
       Psych 100                3               A-
   

   1. Calculate the semester GPA for this student for each semester. (Refer to the chart at www.registrar.umb.edu/grading.html if you need to be reminded of the grade point equivalents of the different letter grades.)

   2. What is this students cumulative GPA at the end of her first year?

   3. The student then took two summer courses, each 2 credits, and earned an A- in each. What is her new cumulative GPA?

3. A UMB student has earned 55 credits toward her degree but has a GPA of just 1.80. The registrar has informed her that she is on probation and must raise her GPA to at least 2.0 after one more semester, or she will be suspended.

   1. If she takes 12 credits, what is the minimum GPA she must earn in that semester to avoid being suspended?

   2. Answer the same question if she takes 9 credits.

   3. What if she took just 6 credits?

   4. (Optional) What would you do if you found yourself in a similar situation - take fewer courses in hopes of doing really well in them, or take more courses so that you could afford to do not quite so well in each?

4. In the example in the new Averages chapter in Common Sense some of the numbers are genuine: they come from the Globe article. But some we made up: the average prices for cars and trucks in each year, and the percentages of each that were sold. Do some research so that you can write a few paragraphs on whether those numbers are more or less correct. (Don't try to redo the computations with better numbers. Just compare what you find with the assumptions we made in the book. Be sure to document the sources of your information.)

5. The Department of Transportation has monitored cars during rush hour traffic and collected the following data:

   	number of riders	percentage of cars
   		1		      60
   		2		      25
   		3		      10
   		4		       5
   

   (These are made up numbers. Some day we'll find real ones.)

   1. What is the average number of riders per car.

   2. What is the average number of riders that each commuter shares a car with?

      Hint. This is another instance of the class size paradox we discussed in class. The first question asks about a typical or average car. The second asks about a typical or average rider. The answer to the second question is larger than the answer to the first.