Python: matplotlib - probability mass function as histogram

Question

I want to draw a histogram and a line plot at the same graph. However, to do that I need to have my histogram as a probability mass function, so I want to have on the y-axis a probability values. However, I don't know how to do that, because using the normed option didn't helped. Below is my source code and a sneak peek of used data. I would be very grateful for all suggestions.

data = [12565, 1342, 5913, 303, 3464, 4504, 5000, 840, 1247, 831, 2771, 4005, 1000, 1580, 7163, 866, 1732, 3361, 2599, 4006, 3583, 1222, 2676, 1401, 2598, 697, 4078, 5016, 1250, 7083, 3378, 600, 1221, 2511, 9244, 1732, 2295, 469, 4583, 1733, 1364, 2430, 540, 2599, 12254, 2500, 6056, 833, 1600, 5317, 8333, 2598, 950, 6086, 4000, 2840, 4851, 6150, 8917, 1108, 2234, 1383, 2174, 2376, 1729, 714, 3800, 1020, 3457, 1246, 7200, 4001, 1211, 1076, 1320, 2078, 4504, 600, 1905, 2765, 2635, 1426, 1430, 1387, 540, 800, 6500, 931, 3792, 2598, 5033, 1040, 1300, 1648, 2200, 2025, 2201, 2074, 8737, 324]
plt.style.use('ggplot')
plt.rc('xtick',labelsize=12)
plt.rc('ytick',labelsize=12)
plt.xlabel("Incomes")
plt.hist(data, bins=50, color="blue", alpha=0.5, normed=True)
plt.show() 

Answer 1

As far as I know, matplotlib does not have this function built-in. However, it is easy enough to replicate

    import numpy as np
    heights,bins = np.histogram(data,bins=50)
    heights = heights/sum(heights)
    plt.bar(bins[:-1],heights,width=(max(bins) - min(bins))/len(bins), color="blue", alpha=0.5)

Edit: Here is another approach from a similar question:

     weights = np.ones_like(data)/len(data)
     plt.hist(data, bins=50, weights=weights, color="blue", alpha=0.5, normed=False)