I have the following data (
prop is like empirical CDF):
td <- data.frame(a = 3:14, prop=c(0, 0, 0.026, 0.143, 0.21, 0.361, 0.535, 0.719, 0.814, 0.874, 0.950, 0.964))
I want to fit a normal CDF using an appropriate mean and standard deviation. How can I find such a mean and a standard deviation value that fits the data above?
mean <- 8.8 # <-- How can I find a best fitting number? sd <- 2.3 # <-- How can I find a best fitting number? x <- seq(from = 2, to = 15, by = .1) cdf <- data.frame(x = x, y = pnorm(q = x, mean = mean, sd = sd)) library(ggplot2) ggplot(data = td, aes(x = a, y = prop)) + geom_point() + geom_line(data = cdf, aes(x = x, y = y))
The motivation behind this question is to replicate a graph I saw on a book. The book used the same proportions and fitted the normal ogive to the data. It looks like normal ogive fitted so well and I couldn't replicate it. There is no way the author used the raw data because the data is from a 100 years old book and the author's book published about 17 years ago. Here is the graph with its caption:
Caption: "Proportions correct on item 46, plotted against age, with a fitted normal ogive."