Calculation query

Question

Hi,
I have a query regarding calculation.Please help me out.
There are 3 exams
Exam1 is out of 30 -In this student obtained 26
Exam 2 is out of 30 -In this student obtained 24
Exam 3 is out of 100 -In this student obtained 70

By combining all these exam marks,we need results out of 50.
Method1:
Converting Exam1 marks to 10% (i.e) 8.67
Converting Exam2 marks to 10% (i.e) 8
Converting Exam3 marks to 30% (i.e) 21
----------------------------------------------------
Marks total: 37.67
so overall 50%(10%+10%+30%)

Method 2:
Converting Exam1 marks to 100% (i.e) 86.7
Converting Exam2 marks to 100% (i.e) 80
Converting Exam3 marks to 100% (i.e) 70
----------------------------------------------------
Marks total: 236.7( out of 300)
Converting to 100: 78.6
Converting to 50 : 39.3


Why the results is varying by these two methods.Please clarify us and tell us which is the correct method.

Answer 1

In the first method you are saying that 70/100 is worth 3 times more than 26/30 or 24/30. However, in the second method you are saying that they are all of equal value. That's why you are getting different answers. You are "weighting" in the first method and "not weighting" in the second method.

method 1

26/30=13/15=43.333/50

24/30=4/5=40/50

70/100=35/50

35+40+43.333=118.333

118.333/3=39.4/50

 

method 2

26/30=13/15=86.666/100

24/30=4/5=80/100

70/100=70/100

86.666+80+70=236.666

236.666/3=78.888

78.888/100=39.444/50

same answer

Answer 2

In a previous comment Jon P. already gave a comprehensive answer with a great deal of explanation, so I am just adding couple thoughts in this regards.

 

By virtue of having the tag "Fractions" associated with this question and making some "qualified guess" it seems that the expected answer would pertain more to fractions arithmetic rather than test "weighting algorithms", so Method 2 would probably take precedence. Furthermore, based on this assumption, the fraction calculations can be performed simply as:

 

(26/30 + 24/30 + 70/100) = 2 11/30 (or 2.366667 as a decimal rounded to 6 digits)

 

and then multiplied by improper fraction 100/6 to get the marks out of 50, resulting in:

 

2 11/30 x 100/6 = 39 4/9 (exact fraction) or 39.444444 written as a decimal rounded to 6 digits.

 

Some logical explanation beyond the computation method. Adding all 3 fraction and dividing the result by 3 essentially will give the average value of the non-weighted test scores, namely: 71/90, or 0.788889 as a decimal number, or the mark 78.889 out of 100. Consequently, dividing the latter by half will result in the mark 39.44 (rounded).

 

Please notice the small rounding error in the original Method 2 calculations due to intermediate fractions-to-decimal conversion. The exact value is provided in my computation method, namely: 39 4/9. In order to simplify the computation I’ve been using the online 3-Fractions calculator, which provides both fraction/decimal results (http://webinfocentral.com/math/fractions.aspx).

 

Hope this may help. Best regards,

Answer 3

In the first method, Exam 3 counts for 30% out of a total of 50%.  That means that Exam 3 by itself counts for 30/50 = 3/5 of the overall score.

 

In the second method, all three tests count equally.

 

You'd expect to get different results if you weight the tests differently.

 

There's no "correct" method.  It depends on how you want the tests to be weighted.  If you want them weighted equally, then the second method is correct, but if you want them weighted some other way (such as when a final exam is considered more important that other exams), then you can apply the weights however you choose.