%pylab inline
%load_ext sympyprinting

import numpy as np

a = np.array([23, 29, 20, 32, 23, 21, 33, 25])
print a.sum()
a.size

mean = a.sum(dtype=float) / a.size
print mean
print np.mean(a)
assert mean == np.mean(a)

print a.sort()
print np.median(a)

np.bincount(a).argmax()
np.angle(

c = np.array([3, 2, 7, 9, 5, 1, 2])
print np.median(c)

c = np.array([5, 6, 6, 2, 9])
print np.mean(c)

c = np.array([2, 5, 10, 9, 2, 9, 4, 9])
np.bincount(c).argmax()

c = np.array([9, 7, 6, 6, 6, 8, 8, 4, 6, 2])
print np.mean(c)

c = np.array([10, 3, 2, 5, 1, 8, 1, 9, 7])
print np.median(c)

c = np.array([8, 6, 5, 9, 10, 1, 2, 4, 10])
np.mean(c)

c = np.array([6, 2, 2, 5, 1, 2, 8, 8])
np.bincount(c).argmax()

c = np.array([4, 7, 1, 9, 8, 6, 1])
np.median(c)

b = (81 + 81 + 81 + 81 + 91) / 5

b

c = np.array([85, 77, 94, 88, 91])
np.mean(c)

c = np.array([82, 82, 82, 82, 100, 100])
np.mean(c)

c = np.array([83, 98, 80, 81, 91, 95])
np.mean(c)

c = np.array([82, 82, 82, 90])
np.mean(c)

c = np.array([92, 88, 86, 95, 97, 76])
np.mean(c)

c = np.array([85, 85, 85, 100, 100])
np.mean(c)

c = np.array([84, 84, 84, 96])
np.mean(c)

d = np.array([14, 6, 3, 2, 4, 15, 11, 8, 1, 7, 2, 1, 3, 4, 10, 22, 20], dtype=float)
boxplot(d, vert=False, )

d = np.array([3, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 9, 9, 10, 11], dtype=float)
boxplot(d, vert=False)

sample = [1, 3, 5, 7, 14]
population_mean = sum(sample)/len(sample)
print population_mean

def population_variance(population):
    mean = np.mean(population)
    pv = sum([(float(i) - mean)**2 for i in population]) / len(population)
    return pv
population_variance(sample)

# Hours of television
sample = [1.5, 4, 1, 2.5, 2, 1]
print 'mean: %s' % np.mean(sample)
print 'variance: %s' % population_variance(sample)

def unbiased_variance(sample):
    mean = np.mean(sample)
    pv = sum([(float(i) - mean)**2 for i in sample]) / (len(sample) - 1)
    return pv
print 'sample variance: %s' % unbiased_variance(sample)

sample = [8,10,16,2,23,4]
print '%.2f years old' % np.mean(sample)
print '%.2f years^2' % population_variance(sample)

sample = [30,17,1,3,11]
print '%.2f years old' % np.mean(sample)
print '%.2f years^2' % unbiased_variance(sample)

sample = [1, 2, 3, 8, 7]

from IPython.display import display, Math, Latex
from sympy.printing.python import python
import sympy as sym
display(Math(latex('\mu = %.2f' % np.mean(sample))))
display(Math(latex('\sigma^2 = %.2f' % population_variance(sample))))
display(Math(latex('s^2_{n-1} = %.2f' % ( unbiased_variance(sample)))))

math.sqrt(7.76)

sample = [30,17,1,3,11]
mean = np.mean([float(i) for i in sample])
print '%.2f' % mean
v = unbiased_variance([float(i) for i in sample])
print '%.2f' % v
print '%.2f' % math.sqrt(v)

sample = [8,10,16,2,23,4]
mean = np.mean([float(i) for i in sample])
print '%.2f' % mean
v = variance([float(i) for i in sample])
print '%.2f' % v
print '%.2f' % math.sqrt(v)

display(Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx'))

from sympy.printing.python import python
import sympy as sym

x, y, z = sym.symbols("x y z")
print latex(Rational(3,2)*pi + exp(I*x) / (x**2 + y))

display(Math(latex('%s^2' % sym.Symbol("s_n"))))