marvelje / dsc-chi-warmup-sampling

warmup after sampling lecture in V2.1

Central Limit Theorem and Sampling

Two great tastes that taste great together

Conceptual Writing

What is the Central Limit Theorem, and how does it enable us to calculate things about statistics?

'''
Your answer here
'''

A spot of coding, eh

#Run this cell without changes

#data manip
import pandas as pd
import numpy as np

#viz
import matplotlib.pyplot as plt

#render matplotlib in jl
%matplotlib inline

#tests
from test_background import pkl_dump, test_obj_dict, run_test_dict, run_test

Import data.csv from the data folder

This is the same data you saw in the API and Pandas checkpoint yesterday

# your code here

Creating a distrbution of means from multiple samples

• Draw 10 random samples from the data of size 250, and for each sample, calculate the mean hourly_rate

  • use a list comprehension (the start of the code is provided for you)
  • use random_state=trial so that we all generate the same samples
    • (why do we assign random_state to a dynamic value?)

• Plot a histogram of the 25 means (does this look like any distribution you've seen?)

  • don't forget titles and labels

#calculate the 10 means of `hourly_rate` from the 25 samples 
#by filling in the code below

hourly_rate_sample_means = [
    insert__code__here
    ['hourly_rate']
    insert__code__here
    for trial 
    in range(0,10)
]

#run this cell to test!

run_test(hourly_rate_sample_means, 'hourly_rate_sample_means')

#plot your histogram here

#no help this time!

Let's do the same thing, but for 30 samples

Under the Don't Repeat Yourself principle, let's create some functions instead of copying and pasting

First, a function to calculate a list of means from samples

Fill in the code below to create a function that:

• takes samples from the imported data
• where the size of the sample is a parameter
• and the number of samples is a parameter
• and random_state for each sample is the sample number
  • so for the first sample random_state is 1, for the second sample random_state is 2, etc.

Then, use the function to assign a list of the means of 30 samples with 250 observations in each sample to the variable means_30

Hint: don't get confused by a parameter of a population and the parameter of a function!

def sample_and_mean(#your code here):
    '''
    takes samples of df and returns list of means of those samples
    
    Parameters:
        sample_size: size of samples to take (int)
        
        sample_number: number of samples to take (int)
        
    output:
        list of sample means
    '''
    
    means = [
    #your code here
    ['hourly_rate']
    #your code here
    for trial 
    #your code here
    ]
    
    return means

means_30 = #your code here

#run this cell to test!

run_test(means_30, 'means_30')

Next, a function to plot the histograms of that list of sample means

We'll use the previous function in this histogram function!

Fill in the code below to create a function that:

• Calls sample_and_mean to generate the data to plot a histogram

• Plots the histogram of the data generated by sample_and_mean

  • Include dynamic titles based on how many samples there are and how many observations in each sample!

Then, call the function to create a histogram of the means of 30 samples with 250 observations each

def sample_and_hist(#your code here):
    
    '''
    samples df multiple times
    
    finds the mean of `hourly_rate` for each sample
    
    creates a histogram of the results
    
    Parameters:
        sample_size: size of samples to take (int)
        
        sample_number: number of samples to take (int)  
        
    output:
        prints a histogram of means of the samples
    '''
 
    means = #your code here

    fig, ax = __insert__code__here
    
    ax.__insert__code__here
    ax.__insert__code__here
    ax.__insert__code__here
    ax.__insert__code__here
    
    plt.show()
    
sample_and_hist(#your code here)

Now that we have this function let's go

Generate three histograms of the means of hourly_rate with:

• 50, 500, and 5000 samples

• 250 observations in each sample

What do you notice?

#your code here

Generate three histograms of the means of hourly_rate with:

• 500 samples each

• 50, 500, and 5000 observations in each sample, respectively

What do you notice?

#your code here