import matplotlib
from datascience import *
%matplotlib inline
import matplotlib.pyplot as plots
import numpy as np
plots.style.use('fivethirtyeight')

# population of size 10

number_of_ones = 2
zero_one_population = np.append(np.ones(number_of_ones), np.zeros(10 - number_of_ones))

print('Standard Deviation:', np.round(np.std(zero_one_population),2))

zero_one_population

def sd_of_zero_one_population(number_of_ones):
    """Returns the SD of a population 
    that has 10 elements: num_ones with value 1 and (10 - num_ones) with value 0"""
    zero_one_population = np.append(np.ones(number_of_ones), 
                                    np.zeros(10 - number_of_ones))
    return np.std(zero_one_population)

possible_ones = np.arange(11)
zero_one_pop = Table().with_columns(
    'Number of Ones', possible_ones,
    'Proportion of Ones', possible_ones / 10
)
zero_one_pop.show()

sds = zero_one_pop.apply(sd_of_zero_one_population, 'Number of Ones')
zero_one_pop = zero_one_pop.with_column('Pop SD', sds)
zero_one_pop.show()

zero_one_pop.scatter('Proportion of Ones', 'Pop SD')