# histogram example

x <- c(1,1,2,3,3,3,4,5,5,6,6,7,8,8,8)

N = 8 # number of bins
# N = ceiling(sqrt(length(x)))

xmax = max(x); xmin = min(x);
range_x = xmax-xmin
cw = range_x/N
cw = floor(cw)+1; #take next largest integer value 
# if data is integer valued

cl <- rep(0,N+1)
cl[1] = xmin

for (i in 1:N){
  cl[i+1]=xmin + (i)*cw
}

delta = 0.5; #offset of bins

cb = cl-delta
bins = cb;
bc = rep(0,N)

for (i in 1:N){
  bc[i]=0.5*(cb[i+1]+cb[i])
}

hist(x,breaks=cb, col='magenta',freq=TRUE)
axis(side=1, at=bc, labels=bc, col.lab="red")