Question

I need a histogram for my data, but could not find one with a curve. Can anyone please suggest a histogram showing frequencies (not densitities) with a curve for the data below? Fancy ones are preferred, but no worries if not 🙂

x <- rnorm(1000)
hist(x)

Answer 1

Here’s the slow, step-by-step version.

This is your data.

population_mean <- 0
population_sd <- 1
n <- 1000
x <- rnorm(n, population_mean, population_sd)

These are some x coordinates for drawing a curve. Notice the use of qnorm to get lower and upper quantiles from a normal distribution.

population_x <- seq(
  qnorm(0.001, population_mean, population_sd), 
  qnorm(0.999, population_mean, population_sd), 
  length.out = 1000
)

In order to convert from density to counts, we need to know the binwidth. This is easiest if we specify it ourselves.

binwidth <- 0.5
breaks <- seq(floor(min(x)), ceiling(max(x)), binwidth)

Here’s our histogram.

hist(x, breaks)

The count curve is the normal density times the number of data points divided by the binwidth.

lines(
  population_x, 
  n * dnorm(population_x, population_mean, population_sd) * binwidth, 
  col = "red"
)

Let’s see that again with the sample distribution rather than the population distribution.

sample_mean <- mean(x)
sample_sd <- sd(x)
sample_x <- seq(
  qnorm(0.001, sample_mean, sample_sd), 
  qnorm(0.999, sample_mean, sample_sd), 
  length.out = 1000
)
lines(
  population_x, 
  n * dnorm(sample_x, sample_mean, sample_sd) * binwidth, 
  col = "blue"
)