I got 30% on a 10-problem test, 70% on a 20-problem test and 80% on a 30-problem test. If the three tests are combined in one 60-problem test what percentage is my overall score?
You can calculate like below:
30% on (10 problem test) = 30% x 10 = 3
70% on (20 problem test) = 70% x 20 = 14
80% on (30 problem test) = 80% x 30 = 24
Total of problems = 41
in (%) = 41 x 100/60= 68.33%
Also, you can calculate in this tool: gradecalculator.tech
30% on the 10 problem test = 30%*10=3
70% on the 20 problem test = 70%*20=14
80% on the 30 problem test = 80%*30=24
=> total right problem is 41.the percentage is 41*100/60=
That result is like adding
3/10 + 14/20 + 24/30 = 41/60
Wow, just adding the numerators and the denominators ! Unfortunately Math doesn't work like that
3/10 + 14/20 + 24/30
= 18/60 + 42/60 + 48/60
= 108/60 for 3 tests
so average = (108÷3)/60 = 36/60 = 60%
By simply adding the numerator and denominators you are "weighting" the tests.
This is a major topic in statistics.
There are also many on-line calculators to calculate marks weighed differently.
Here is one of them:
http://www.rapidtables.com/calc/grade/grade-calculator.htm
Notice also by simply averaging the 3 percentages we get 60% as well. That is because percentages all have the same denominator of 100, so the normally erroneous method of just adding the numerators and denominators does work.
i.e.
average of (30/100 + 70/100 + 80/100)
---> 180/300 = .6 or 60%
Without knowing what the weight factors are this question can't really be answered.
To find the overall percentage score, we need to calculate the weighted average of the three test scores.
The first step is calculating the weight for each test score. Since the tests have different numbers of problems, we can use the number of problems as the weights. In this case, the first test had 10 problems, the second test had 20 problems, and the third test had 30 problems.
Next, we need to calculate the weighted score for each test. To do this, we multiply each test score by its corresponding weight.
For the first test:
Weighted score = 30% (0.3) * 10 = 3
For the second test:
Weighted score = 70% (0.7) * 20 = 14
For the third test:
Weighted score = 80% (0.8) * 30 = 24
Now, we add up the weighted scores:
Total weighted score = 3 + 14 + 24 = 41
Finally, we calculate the overall percentage score by dividing the total weighted score by the total number of problems in the combined test (60) and multiplying by 100:
Overall percentage score = (41/60) * 100 ≈ 68.3%
Therefore, your overall percentage score on the combined 60-problem test is approximately 68.3%.