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

import warnings
warnings.simplefilter(action='ignore')

united = Table.read_table('united.csv')
united_bins = np.arange(-20, 300, 10)
united.hist('Delay', bins=united_bins)

delays = united.column('Delay')
population_mean = np.mean(delays)
population_sd = np.std(delays)
population_mean, population_sd

def one_sample_mean(sample_size):
    """Take a sample from the population of flights and compute its mean"""
    sampled_flights = united.sample(sample_size)
    return np.mean(sampled_flights.column('Delay'))

def ten_thousand_sample_means(sample_size):
    """Approximate the distribution of the sample mean"""
    means = make_array()
    for i in np.arange(10000):
        mean = one_sample_mean(sample_size)
        means = np.append(means, mean)
    return means

sample_means_400 = ten_thousand_sample_means(400)
Table().with_column('Mean of 400 flight delays', sample_means_400).hist(bins=20)
print('Population Average:', population_mean)

np.mean(sample_means_400), population_mean

united.num_rows

# How many possible samples are there?
united.num_rows ** 400

sample_means_900 = ten_thousand_sample_means(900)

means_tbl = Table().with_columns(
    '400', sample_means_400,
    '900', sample_means_900
)

means_tbl.hist(bins = np.arange(5, 31, 0.5))
plots.title('Distribution of Sample Average');

"""Empirical distribution of random sample means"""
def plot_sample_means(sample_size):
    sample_means = ten_thousand_sample_means(sample_size)
    sample_means_tbl = Table().with_column('Sample Means', sample_means)
    
    # Print some information about the distribution of the sample means
    print("Sample size: ", sample_size)
    print("Population mean:", population_mean)
    print("Average of sample means: ", np.mean(sample_means))
    print("Population SD:", population_sd)
    print("SD of sample means:", np.std(sample_means))

    # Plot a histogram of the sample means
    sample_means_tbl.hist(bins=20)
    plots.xlabel('Sample Means')
    plots.title('Sample Size ' + str(sample_size))

plot_sample_means(100)

# Sample size 100
# population_SD / SD_of_sample_means
39.48 / 3.998

plot_sample_means(400)

# Sample size 400
# population_SD / SD_of_sample_means
39.48 / 1.992

plot_sample_means(625)

# Sample size 625
# population_SD / SD_of_sample_means
39.48 / 1.567

39.48 / np.sqrt(100)

39.48 / np.sqrt(400)

39.48 / np.sqrt(625)

# Warning: this cell will take a long time to run!
sample_sizes = np.arange(100, 950, 50)

sample_mean_sds = make_array()
for n in sample_sizes:
    sample_means = ten_thousand_sample_means(n)
    sample_mean_sds = np.append(sample_mean_sds, np.std(sample_means))

sd_table = Table().with_columns(
    'Sample size', sample_sizes,
    'SD of simulated sample means', sample_mean_sds,
    'Pop SD / sqrt(sample size)', population_sd / np.sqrt(sample_sizes),
)
sd_table

sd_table.scatter('Sample size')

sf_salaries = Table.read_table("san_francisco_2019.csv")
sf_salaries.hist("Salary")

def one_sample_mean(sample_size):
    """Take a sample from the population of flights and compute its mean"""
    sampled_salaries = sf_salaries.sample(sample_size)
    return np.mean(sampled_salaries.column('Salary'))

def ten_thousand_sample_means(sample_size):
    """Approximate the distribution of the sample mean"""
    means = make_array()
    for i in np.arange(10000):
        mean = one_sample_mean(sample_size)
        means = np.append(means, mean)
    return means

sample_means_400 = ten_thousand_sample_means(400)
Table().with_column('Mean of 400 salaries', sample_means_400).hist(bins=20)
print('Population Average:', np.mean(sf_salaries.column("Salary")))