In exams: Automatic Generation of Exams in R

## DATA
n <- sample(30:50, 1)
m <- sample(1:4, 1)
s <- runif(1, 0.5, 2)
delta <- ifelse(runif(1) < 0.2, sample(8:12), 0)
p2 <- runif(1, 0.45, 0.55)
skewed <- left <- FALSE
if(!delta) {
    skewed <- runif(1) < 0.6
    left <- runif(1) < 0.3
}

dgpBoxhist <- function(n = 40, mean = 0, sd = 1, delta = 0,
  p2 = 0.5, skewed = FALSE, left = FALSE)
{
  SK <- function(x) abs(diff(diff(fivenum(x)[2:4]))/diff(fivenum(x)[c(2, 4)]))
  sim <- function(x){
    x <- rnorm(n)
    if(skewed) exp(x) else x
  }

  x <- sim()
  if(skewed) while(SK(x) < 0.7) x <- sim() else while(SK(x) > 0.15) x <- sim()
  if(left) x <- -x

  x <- mean + sd * scale(x)
  k <- sample(1:n, round(p2 * n))
  x[k] <- x[k] + delta
  as.vector(sample(x))
}
x <- round(dgpBoxhist(n = n, mean = m, sd = s, delta = delta, 
  p2 = p2, skewed = skewed, left = left), digits = 2)

b <- boxplot(x, plot = FALSE)
spread <- tol <- signif(diff(range(c(b$stats, b$out)))/25, 1)

write.csv(data.frame(x), file = "boxhist.csv", quote = FALSE, row.names = FALSE)

## QUESTION/SOLUTION
questions <- solutions <- explanations <- rep(list(""), 6)
type <- rep(list("schoice"), 6)

questions[[1]] <- paste("The distribution is ", c("", "_not_ "), "unimodal.", sep = "")
solutions[[1]] <- c(delta < 1, delta > 1)

questions[[2]] <- paste("The distribution is", c("symmetric.", "right-skewed.", "left-skewed."))
solutions[[2]] <- c(!skewed, skewed & !left, skewed & left)

questions[[3]] <- paste("The boxplot shows ", c("", "_no_ "), "outliers.", sep = "")
solutions[[3]] <- c(length(b$out) > 0, length(b$out) < 1)

questions[[4]] <- "A quarter of the observations is smaller than which value?"
solutions[[4]] <- explanations[[4]] <- signif(b$stats[[2]], 3)
type[[4]] <- "num"

questions[[5]] <- "A quarter of the observations is greater than which value?"
solutions[[5]] <- explanations[[5]] <- signif(b$stats[[4]], 3)
type[[5]] <- "num"

questions[[6]] <- paste("Half of the observations are",
  sample(c("smaller", "greater"), 1), "than which value?")
solutions[[6]] <- explanations[[6]] <- signif(b$stats[[3]], 3)
type[[6]] <- "num"

explanations[1:3] <- lapply(solutions[1:3], function(x) ifelse(x, "True", "False"))
solutions[1:3] <- lapply(solutions[1:3], mchoice2string)
if(any(explanations[4:6] < 0)) explanations[4:6] <- lapply(solutions[4:6], function(x) paste("$", x, "$", sep = ""))

Question

For the r n observations of the variable x in the data file boxhist.csv draw a histogram, a boxplot and a stripchart. Based on the graphics, answer the following questions or check the correct statements, respectively. (Comment: The tolerance for numeric answers is $\pmr tol$, the true/false statements are either about correct or clearly wrong.)

answerlist(unlist(questions), markup = "markdown")

Solution

par(mfrow = c(1, 2))
boxplot(x, axes = FALSE)
axis(2, at = signif(b$stats, 3), las = 1)
box()
hist(x, freq = FALSE, main = "")
rug(x)

answerlist(unlist(explanations), markup = "markdown")

Meta-information

extype: cloze exsolution: r paste(solutions, collapse = "|") exclozetype: r paste(type, collapse = "|") exname: Boxplot and histogram extol: r tol