Calculating grades in r

Question

I am calculating final averages for a course. There are about 500 students, and the grades are organized into a .csv file. Column headers include:

Name, HW1, ..., HW10, Quiz1, ..., Quiz5, Exam1, Exam2, Final

Each is weighted differently, and that shouldn't be an issue programming. However, the lowest 2 HW and the lowest Quiz are dropped for each student. How could I program this in r? Note that the HW/Quiz dropped for each student may be different (i.e. Student A has HW2, HW5, Quiz2 dropped, Student B has HW4, HW8, Quiz1 dropped).

Answer 1

Here is a simpler solution. The sum_after_drop function takes a vector x and drops the i lowest scores and sums up the remaining. We invoke this function for each row in the dataset. ddply is overkill for this job, but keeps things simple. You should be able to do this with apply, except that you will have to convert the end result to a data frame.

The actual grade calculations can then be carried out on dd2. Note that using the cut function with breaks is a simple way to get letter grades from the total scores.

library(plyr)
sum_after_drop <- function(x, i){
  sum(sort(x)[-(1:i)])
}

dd2 = ddply(dd, .(Name), function(d){
  hw = sum_after_drop(d[,grepl("HW", nms)], 1)
  qz = sum_after_drop(d[,grepl("Quiz", nms)], 1)
  data.frame(hw = hw, qz = qz)
})

Answer 2

Here's a sketch of how you could approach it using the reshape2 package and base functions.

#sample data
set.seed(734)
dd<-data.frame(
    Name=letters[1:20],
    HW1=rpois(20,7),
    HW2=rpois(20,7),
    HW3=rpois(20,7),
    Quiz1=rpois(20,15),
    Quiz2=rpois(20,15),
    Quiz3=rpois(20,15)
)

Now I convert it to long format and split apart the field names

require(reshape2)
mm<-melt(dd, "Name")
mm<-cbind(mm,
    colsplit(gsub("(\\w+)(\\d+)","\\1:\\2",mm$variable, perl=T), ":",
    names=c("type","number"))
)

Now i can use by() to get a data.frame for each name and do the rest of the calculations. Here i just drop the lowest homework and lowest quiz and i give homework a weight of .2 and quizzes a weight of .8 (assuming all home works were worth 15pts and quizzes 25 pts).

grades<-unclass(by(mm, mm$Name, function(x) {
    hw <- tail(sort(x$value[x$type=="HW"]), -1);
    quiz <- tail(sort(x$value[x$type=="Quiz"]), -1);
    (sum(hw)*.2 + sum(quiz)*.8) / (length(hw)*15*.2+length(quiz)*25*.8)
}))
attr(grades, "call")<-NULL   #get rid of crud from by()
grades;

Let's check our work. Look at student "c"

   Name HW1 HW2 HW3 Quiz1 Quiz2 Quiz3
      c   6   9   7    21    20    14

Their grade should be

((9+7)*.2+(21+20)*.8) / ((15+15)*.2 + (25+25)*.8) = 0.7826087

and in fact, we see

grades["c"] == 0.7826087

Answer 3

Here's a solution with dplyr. It ranks the scores by student and type of assignment (i.e. calculates the rank order of all of student 1's homeworks, etc.), then filters out the lowest 1 (or 2, or whatever). dplyr's syntax is pretty intuitive—you should be able to walk through the code fairly easily.

# Load libraries
library(reshape2)
library(dplyr)

# Sample data
grades <- data.frame(name=c("Sally", "Jim"),
                     HW1=c(10, 9),
                     HW2=c(10, 5),
                     HW3=c(5, 10),
                     HW4=c(6, 9),
                     HW5=c(8, 9),
                     Quiz1=c(9, 5),
                     Quiz2=c(9, 10),
                     Quiz3=c(10, 8),
                     Exam1=c(95, 96))

# Melt into long form
grades.long <- melt(grades, id.vars="name", variable.name="graded.name") %.%
  mutate(graded.type=factor(sub("\\d+","", graded.name)))
grades.long

# Remove the lowest scores for each graded type
grades.filtered <- grades.long %.%
  group_by(name, graded.type) %.%
  mutate(ranked.score=rank(value, ties.method="first")) %.%  # Rank all the scores
  filter((ranked.score > 2 & graded.type=="HW") |  # Ignore the lowest two HWs
         (ranked.score > 1 & graded.type=="Quiz") |  # Ignore the lowest quiz
         (graded.type=="Exam"))
grades.filtered

# Calculate the average for each graded type
grade.totals <- grades.filtered %.%
  group_by(name, graded.type) %.%
  summarize(total=mean(value))
grade.totals

# Unmelt, just for fun
final.grades <- dcast(grade.totals, name ~ graded.type, value.var="total")
final.grades

You technically could add the summarize(total=mean(value)) to the grades.filtered data frame rather than making a separate grade.totals data frame—I separated them into multiple data frames for didactical reasons.