So a friend of mine had her grade drop because her teacher had decided to drop the lowest grade. Is this possible or did the teacher mess up something? And if so, then how is it possible. We've figured that the most likely scenario was due to the way assignments are weighted.
Edit To clarify the question a little and give it a more mathematical tone.
Suppose $\{\{a_{i,j}\}_{i=0}^{n}\}_{j=0}^m$ is a list of lists of positive scores (think of these as test scores of $m$ students. Wlog assume that all the scores are in $[0,100]$. Further let $\{w_i\}_{i=0}^n$ be a vector of weights $w_i\in[0,1]$. Let the final grade for student $j$ be the obvious $g_j=\frac{\sum_{i=0}^n w_i a_{i,j}}{\sum_{i=0}^n w_i 100}$.
Is it possible that by dropping the worst score a students score could become worse?
Bonus: What if we grade on a curve (here the answer is pretty much certainly yes), is there some obvious way to fix this problem?
Removing the lowest entry in a list will raise the mean of what is left. Let $S$ be the sum of $n$ items and $a$ the minimum item in the list. The mean before dropping is $\frac Sn$. The mean after dropping is $\frac{S-a}{n-1}$. We have $\frac{S-a}{n-1}-\frac Sn=\frac {S-na}{n(n-1)} \gt 0$ as long as $a$ is less than the original mean.
The way the grade might drop is if her grades are all reasonably uniform, so dropping the lowest grade doesn't change the average much, while other students have one terrible grade. Her ranking in the class could go down in this case, even if her percentage average rises a bit.