I\'m confused. Help. Ok so I\'m calculating my grade.. there\'s 4 categories of

Question

I'm confused. Help. Ok so I'm calculating my grade.. there's 4 categories of grades each category is worth 20% for a total of 80%. If everything is 20% shouldn't I just be able to add up all of the grades and divide by the total and then multiple that by .8 or 80%? I get a different number when I do this method versus when I average each category separately and multiply by .2 or 20 percent then add all of these results together? Why is this?
I'm confused. Help. Ok so I'm calculating my grade.. there's 4 categories of grades each category is worth 20% for a total of 80%. If everything is 20% shouldn't I just be able to add up all of the grades and divide by the total and then multiple that by .8 or 80%? I get a different number when I do this method versus when I average each category separately and multiply by .2 or 20 percent then add all of these results together? Why is this?
I'm confused. Help. Ok so I'm calculating my grade.. there's 4 categories of grades each category is worth 20% for a total of 80%. If everything is 20% shouldn't I just be able to add up all of the grades and divide by the total and then multiple that by .8 or 80%? I get a different number when I do this method versus when I average each category separately and multiply by .2 or 20 percent then add all of these results together? Why is this? I'm confused. Help. Ok so I'm calculating my grade.. there's 4 categories of grades each category is worth 20% for a total of 80%. If everything is 20% shouldn't I just be able to add up all of the grades and divide by the total and then multiple that by .8 or 80%? I get a different number when I do this method versus when I average each category separately and multiply by .2 or 20 percent then add all of these results together? Why is this?

Explanation / Answer

See these examples. You will get the concept.

Suppose you have a class with only a midterm and a final xam. The midterm is 40 percent of the grade, and the xam is 60%. You got an 80 on the midterm and a 100 on the xam. What's your overall grade? Certainly not a 90! If it were a 90, that would be giving the midterm the same weight as the final xam. It seems like you deserve better than a 90, since you got 100 on a test that was worth more than the test you got an 80 on.

Here's the exact calculation:

80 * (40/100) + 100 * (60/100)
32 + 60
92

So, your overall grade is a 92; that's more like it. In general, if you get "M" points on the midterm, and the midterm is "m" percent of the total, and similarly you get E on the xam, which is worth "e" percent, your overall grade is:

M * m + E*e

Note that that formula works as long as m+e=1.0. In other words, they are fractions of the whole. If they don't add up to 1, we have to divide by their total. This is called "normalizing." Here's the more general formula:

(M * m + E*e) / (m+e)

Let's re-do the first one using this idea, only this time we'll have m=40 and e=60:

(80 * 40 + 100 * 60) / (40+60)

(3200 + 6000) / (100)
9200/100
92

And

Suppose that these are your grades:

To find your overall average, you have to compute your test average, your homework average, and so forth. These are each simple averages, without weights, since, for example, all the tests count the same:

Now, we can compute the overall average, which is a weighted average of these numbers:

95*0.4+95*0.1+90*0.2+90*0.3
38+9.5+18+27
92.5

Each category has same weightage, each score doesn't. So, average should be taken.

category scores tests 80 90 homework 90 95 100 programs 70 100 100 xam 90

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