On Fri, 30 Apr 2004 15:04:22 GMT, the renowned alpinekid
wrote:
Spehro Pefhany wrote:
On Fri, 30 Apr 2004 09:22:18 -0400, the renowned Kingfish
wrote:
I come to the experts on everything I can think of help. My
teacher-wife asked me if she was calculating this correctly. I didn't
think so. What's the answer and why/how?
Chapter tests count for 60% of the final grade. Mid-term and final
tests count for 40% of the final grade. Scores for chapter tests were
80, 50 and 69. Mid-term and final tests were 80 and 90. What is the
final grade. One of us says 73.8 and the other says 80.7
Thanks
Okay, let's assume the chapters are *equally* weighted (with each
other), as are mid-term and finals. These are assumptions. And all out
of 100, natch.
1So there are 3 chapter tests, each would count for 60/3 = 20%, and
two
exams, which would count for 40/2 = 20% each as well. That's easy.
Just multiply each score by 0.2 and add, or to put it another way,
it's less calculation to just add up all the scores and divide by 5.
I get 73.8% for the example given.
Best regards,
Spehro Pefhany
I think that your answer of "add it up and divide by 5" only works because the
number of tests is the same ratio as the weighting.
Yes, that is correct, as I hope I explained. Being inherently lazy and
concerned with entry errors, I try to simplify things before crunching
numbers (and by using an RPN calculator, of course).
You can see this by taking
an extreme case. Suppose there were 100 chapter tests and only two term tests,
this would not be right.
The formula should be:
grade = ((sum(chapter tests)/number of chapter tests)*weight)+((sum(term
tests)/(number of term tests)*weight)
This only works if the chapter tests and the exams are weighted
equally with each other.
The general answer is
n
---
\
G= | Wi * Si
/
---
i=0
Where Wi is the weight of each individual score (0 = Wi = 1.0)
Si is each score (all must be out of 100, or at least the same
number). Wi has the characteristic that
n
---
\
1.0= | Wi
/
---
i=0
In this case, Wi = 0.2 for i=0..5, so it can be simplified to:
5
---
\
G= 0.2* | Si
/
---
i=0
You get the same answer but this equation works for any number of tests and any
weighting.
With the above assumption. It's also possible, for example, that the 3
chapter exams add up to 60%, but they are not equal.
73.78= (((80+50+69)/3)*.60)+(((80+90)/2)*.4)
I hope I didn't just do some high schoolers homework:-)
Al
Oh, well.
Best regards,
Spehro Pefhany
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