What’s my final grade?

Question

My grade starts at 98 but it lowered after I took two test both worth 60% in one I got 78 and the other a 69. I took a Final and it was worth 10% I got a 94 what will be my final grade?

Answer 1

Assuming you haven't left any other information out, you're final score will be about an 83.

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Well, assuming there are not any additional points/credit awarded for participation or other things, the best way to estimate your grade is like this.

You started at a 98. Let's assume this was 30% of your grade. (Because you list two exams worth a cumulative of 60% and a final worth 10%, leaving only 30% remainder).

There are several ways we could solve this distribution, but I'm actually going to do it visually. Imagine we are dividing your final grade into 10 chunks (or "bins"). Your distribution might look like this:

98

98

98

78

78

78

69

69

69

94

If we find the mean, we'll find your final grade given the information provided.

829/10 = 82.9 ~ 83

So, your approximate final score is an 83 based on the information provided.

What if we wanted to solve this as an equation instead?

You don't say if the cumulative 60% over the two exams is evenly distributed, so in both of these cases I'm assuming it is.

0.3*98 + 0.6*((78+69)/2) + 0.1*94 = 82.9

Notice that (78+69)/2 is the mean of those two exams, so it's the mean that is worth 60% here. If they weren't worth the same percentage, we'd solve this differently. Let's pretend that the score of 78 was worth 20% whereas the 69 was worth 40%. In that case, we'd solve with:

0.3*98 + 0.2*78 + 0.4*69 + 0.1*94 = 82

And, of course, you'd have done a little worse overall!