python - Hist in matplotlib: Bins are not centered and proportions not correct on the axis

Question

take a look at this example:

 import matplotlib.pyplot as plt
 l = [3,3,3,2,1,4,4,5,5,5,5,5,5,5,5,5]
 plt.hist(l,normed=True)
 plt.show()

The output is posted as a picture. I have two questions:

a) Why are only the 4 and 5 bins centered around its value? Shouldn't the others be that as well? Is there a trick to get them centered?

b)Why are the bins not normalised to proportion? I want the y values of all the bins to sum up to one.

Note that my real example contains much more values in the list, but they are all discrete.

Answer 1

You should adjust the keyword arguments of the plt.hist function. There are many of them and the documentation can help you answer many of these questions.

a. ) You can pass the keywords bins=range(1,7) and align=left. Setting the bins keyword to a sequence gives the borders of each bin. For example, [1,2], [2,3], [3,4], ..., [5, 6].

b. ) Check your bin widths (rwidth!=1). From the matplotlib.pyplot.hist documentation:

If True, the first element of the return tuple will be the counts normalized to form a probability density, i.e., n/(len(x)*dbin). In a probability density, the integral of the histogram should be 1; you can verify that with a trapezoidal integration of the probability density function:

This means that the area under your bins is summing up to one, but because the bin widths are less than 1, the heights get normalized in such a way that the heights don't add up to 1. If you adjust rwidth=1, you get a good looking plot:

plt.hist(l, bins=range(1,7), align='left', rwidth=1, normed=True)