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I have a fifteen point grading system [1...15], where the expectations:

  • 5% of the population is less than 5
  • 10% of the population is greater than 10
  • remaining population is centered around 8

It is easy enough to plot a histogram of my frequency but I want to plot a couple of curves over the top of this histogram

  • a curve to represent an expected normal distribution using the full range (1-15) with a mean of 8 and a sd of 2
  • a second curve showing an expected normal distribution using the effective/practical range 5-10 with a mean of 8 and a sd of 1

I haven't used R in years and am struggling a bit. Here is where I am at:

grades <-c(6,6,5,5,8,8,8,8,9,9,9,9,1,5,5,5,5,5,5,5,13,15)
xbar <-  mean(g)
sdev <-  sd(g)

plotCurve <- function(discreteRangeMin, discreteRangeMax, targetMean, targetDev, color) {
  granularityFactor <- 4
  xfit <- seq(discreteRangeMin, discreteRangeMax, length=discreteRangeMax * granularityFactor)
  yfit <- dnorm(xfit, mean = targetMean, sd = targetDev)  
  plot(xfit, yfit, type='l', axes=F, xlab='', ylab='', col=color)
  return (yfit)
}

plotHist <- function(g, title) {
  zeroThrough15 <- seq(0, 15, length = 16)
  hist(g, breaks=zeroThrough15, freq=T, main=title )
  axis(side=1, at=zeroThrough15, labels=zeroThrough15)
}

# main histogram
title <- paste('Distribution [mean=', round(xbar, 2) , '',  ', sd=', round(sdev, 2), ']', sep='')
plotHist(grades, title)

# add the expected 'full'  distribution over the entire range 
par(new=T)
yfit <- plotCurve(1, 15, targetMean=8, targetDev=2, 'green') 
axis(side=4, at = pretty(range(yfit)))

# add the expected 'practical' distribution over typical range 
par(new=T)
yfit2 <- plotCurve(5, 10, targetMean=8, targetDev=0.5, 'red')

Issues

  • The second curve isn't what I was expecting. I only want it to extend over the range 6-13
  • A third curve that carves out the expected distribution with 5% < 5, the 10% > 10, and ~normal distribution between 5-10 with 85% percent
  • lastly how do I get the labels under the histogram to line up with the buckets better?
akaphenom
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  • I will gladly close if we feel it is a duplicate. Here I am asking a question on approach as well. Let me investigate the other further though. THanks – akaphenom Dec 09 '17 at 18:08
  • Where is your expected domain of 6-13 specified? How are you coming up with that domain? That seems pretty arbitrary (and asymmetric) to me. (It probably doesn't matter, you just need to know how to control the domain on the x-axis, right?) – r2evans Dec 09 '17 at 18:20

0 Answers0