An etude is a short musical composition intended for intensive practice on a particular skill. My R-tudes are similar exercises to help me develop my R skills.

library(tidyverse)

Let’s say you have a large population of people, each of differing abilities on a scale from 0 to 1, and let’s start with the assumption that it’s completely random. Some people are higher, some lower, and the number at each level are roughly equal.

d <- runif(10000)
qplot(d,bins = 10, binwidth = 0.1, geom = "histogram", fill = I("blue"), col = I("black"), alpha = I(0.5))

It’s random, so you have roughly the same number of items in each histogram bucket.

This kind of distribution makes sense in, say, a world where people are choosing a number from 1 to 100 or something completely random. But that’s not a typical real world situation. A more typical example might involve, say, height:

people_data <- data_frame(height = rnorm(100000,mean = (78.9 + 68.5) / 2, sd = (2.24 + 2.16) /2),
                     person = 1:100000)

## Warning: `data_frame()` is deprecated as of tibble 1.1.0.
## Please use `tibble()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

ggplot(data = people_data, aes(height)) +
  geom_histogram(fill = "blue", col = "black", alpha = 0.5, bins = 20, breaks = seq(50,100)) +
  labs(title = "Histogram for height")

The spread of the curve depends on the standard deviation. The standard error of the mean for Americans is about 2.2 according to the CDC.

pop_size = 10000


people_data <- data_frame(person = 1:pop_size,
                          group = factor(ifelse(rbinom(1:pop_size,1,.5),"M","F")),
                          height = rnorm(pop_size,mean = (78.9 + 68.5) / 2, sd = (2.24 + 2.16) /2)
                          )

m <- people_data[people_data$group == "M",]$height %>% length()
f <- people_data[people_data$group == "F",]$height %>% length()


people_data[people_data$group=="M","height"] <- rnorm(m,mean=78.9,sd=10)
people_data[people_data$group=="F","height"] <- rnorm(f,mean=68.5,sd=10)


ggplot(data = people_data, aes(height,fill=group)) +
  geom_histogram( col = "black", alpha = 0.5, bins = 20, breaks = seq(50,100)) +
  labs(title = "Histogram for height") 

ggplot(data = people_data, aes(height,fill = group)) +
  geom_density(alpha = 0.3)