I have five numbers, three of them each represent 25% of an average and the last two are the remaining 25%. One the last two numbers is 10% and the other 15%, how do I add them up into one number ?
I have 35 students. One of them has the following grades : 7, 12, 17, 13 and 15. The first three are out of 25% so no problem, but the 13 is out of 15% and the 15 is out of 10%. How do I add them up to make a grade out of 25% ?
I know this is beyond easy for some, so thank you for your help.
If you want a percentage as the end result, $$((g_1+g_2+g_3)\times 0.25 + g_4\times 0.1 + g_5\times 0.15)\times 100$$
Where the $g_i$ are the grades as a percentage out of $100$ i.e. if the student got $20/25$ for the first grade, then $g_1 = 80$.
If you just change all the results to be out of $25$ then you loose information about the relative weighting of each grade, because a test/assignment marked out of $25$ should (often is) weighted more than when it is out of say $10$.
If this is not an issue, then you can just add the scores together from the $10\%$ and $15\%$ tasks as the fourth percentage.
In this case the formula for the weighted mean is
$$ \frac{25}{100} \cdot 7 + \frac{25}{100} \cdot 12 + \frac{25}{100} \cdot 17 + \frac{15}{100} \cdot 13 + \frac{10}{100} \cdot 15 = 12.45 $$
If you want to write one grade with weight 25% that combines the last two grades, the formula is
$$ \frac{15}{100} \cdot 13 + \frac{10}{100} \cdot 15 = \frac{25}{100} \cdot x \implies x = \frac{15 \cdot 13 + 10 \cdot 15}{25} = 13.8$$
If you double check now, you get that the average of $7,12,17$ and $13.8$ is $12.45$ (so that each grade is worth 25%).
