May 5- Weighted averages

One beautiful thing about my job is that everything happens in cycles.  A semester begins, a semester ends. There's a certain comfort in knowing that no matter how weird my teaching schedule is, or if there's a time-consuming student or two, that in a few months, all of that will change. I will have a different but equally weird teaching schedule, and a different but equally time-consuming student.

I teach, I test, I grade. There's a bit of zen in all of that.

It is nearing the end of the spring semester.  There is one question I get over and over again, so I thought I'd address it here.

"What do I need to get on the (last graded assignment of choice) to get an A/pass the class?"

This is a concept that most students struggle a bit with, and it isn't hard, you just have to think about weighted averages.

You know that to find an average, or the mean of a set of values, you would simply add those values together, then divide the sum by the number of values you added.  Well, a weighted average takes into account that not every assignment given in a course is weighted evenly.

In order to calculate the weighted average, you multiply each score by the weight it carries as a decimal.

For instance, Tommy has an average of 75% on his homeworks which are worth 10%.  He had an average of 84% on the quizzes which are worth 15%.  The exams were all worth 25%, and he got a 90% on the first exam, an 80% on the second exam, and hasn't yet taken the last exam.

So, Tommy needs to set up what he has:
(75)(.10)+(84)(.15)+(90)(.25)+(80)(.25)=62.5

So, if he skips taking the last test, he would receive a D in the class. That's not good enough! Tommy wants an A! Well, even if he geta a perfect score on the last test, that isn't possible.

62.5+(100)(.25)=87.5 that's a B.

Hrmmm, Tommy thinks. Well, if the best he can do is a B, what's the lowest grade he could get on the test to get that B? Just replace the test score with a variable, and solve.

62.5 + .25x = 80
-62.5                 -62.5

.25x = 17.5
/.25        /.25

X = 70

As long as Tommy gets a 70 on the test, he'll have that B.

So, clearly, if the last assignment is worth 20% of the overall grade, then how well a student does on that assignment could have a big impact on the overall grade.  But if the last assignment is only worth 5% of the overall grade, well, it's not such a big deal.

It's funny, students will get all worked up about a little assignment, but flake off during the big assignments.  For example, a student who came into my office today told me that he was so busy completing the extra credit problems (worth 10 points) that he forgot to study for the exam (worth 100 points).  See the problem?

But honestly, it's not just students and grades.  

I'm guilty, too.

What is worth the most? 

Tonight's post is late because I was taking care of high point things today: work, a run, making great food, spending this evening with my love.

The rest can wait for tomorrow!