For some purpose I found myself generating and analyzing the average of the combinations of a set and when I generated the corresponding histogram I was surprised by its shape.
It should be remembered that the combinations C(m, n) of a set are the number of subsets of a set of m elements taken from n in n.
The number of combinations is calculated with:
This is the very simple code to generate the combinations, calculate their mean and generate the histogram:
m <- 50
n <- 6
COMBINATIONS <- t(as.data.frame(combn(m,n)))
C_M <- apply(COMBINATIONS, 1, mean)
hist_all <-hist(C_M, breaks = length(unique(C_M)), col = “blue”)
Interesting histogram. It’s as if there are two distributions.
But if we change the value of m by:
m <- 50
n <- 4
We obtain the following histogram:
Although it is a very simple math and programming exercise, the interesting thing is to interpret why histograms behave this way, so it becomes an exercise in understanding the visualization.