Pipe some data to this script to plot a data set vs benford's law.

benford.py

# Pipe some data to stdin. Each line should contain a number.
import csv
from collections import defaultdict
from math import log10
import matplotlib
import matplotlib.pyplot as plt
import functools

import fileinput

# We care about digits 1-10
digits = set(map(str, range(1, 10)))

def log_frequency(frequencies, line):
    """Increment the frequency in the dict for {digit: count}."""
    input_digits = [int(x) for x in line if x in digits]
    if input_digits:
        frequencies[input_digits[0]] = frequencies.get(input_digits[0], 0) + 1
    return frequencies

# Scaling
data = functools.reduce(log_frequency, fileinput.input(), {})
total_numbers = sum(data.values())
data = sorted([(count / float(total_numbers), d) for (d, count) in data.items()], reverse=True)

# Comparison
benford = [(log10(1 + 1.0 / i), str(i)) for i in range(1, 10)]

# Plot first digit distribution vs. Benford
plt.plot([x[0] for x in data], label='Data Set')
plt.plot([x[0] for x in benford], label="Benford's Law", linewidth=10, alpha=0.23)

plt.ylabel("Distribution probability", fontsize=14)
plt.xlabel("First digit for %s numbers" % total_numbers, fontsize=14)
plt.title("Check it out yo\n", fontsize=12)
plt.xticks([x for x in range(len(benford))], [int(x[1]) for x in benford])
plt.legend()
plt.show()