Generating a skewed bell curve of random data in R

r-random-grades.R

minVal <- 0
maxVal <- 100
medVal <- 70
numRows <- 1000000

adjMax <- maxVal - minVal
adjMed <- medVal - minVal
# Generate a vector that sets how likel
# each value is to be chosen.

# An exponent that will convert 0.5
# to our desired median
skew <- log(0.5, base = adjMed / adjMax)
# For each possible value in the interval,
# we look up the corresponding probabili!y
# in a normal distribution of 0 to 1,
# shifted by that skew factor
skew_prob <- dnorm(
  seq(0, 1, length.out = adjMax + 1) ^ skew,
  mean = 0.5,
  # Stddev of 1/3 mean avg, makes 99.7% of values between
  # 0 and 1.
  sd = 0.5 / 3
)
# Now pick a number from minVal to maxVal
# once for each numRows. The prob of
# picking each value is adjusted by the
# probability map we calculated earlier.
x <- sample(
  minVal : maxVal,
  size = numRows,
  replace = TRUE,
  prob = skew_prob
)

stanine <- c(0, 4, 11, 23, 40, 60, 77, 89, 96) / 100
q <- quantile(x, stanine, type=1, na.rm = TRUE)
s <- sapply(
  x,
  function(i){
    as.character(sum(q <= i))
  }
)

d <- data.frame(score = x, sta = s)

library(ggplot2)
ggplot(d) +
  geom_histogram(aes(score, fill = sta), binwidth=1)