chapter 3: Describing Data With Statstics

이 장에서는 통계치를 가지고 한번 파이썬 코드를 짜보자.

3.1 Finding the Mean

>>> shortlist = [1, 2, 3]
>>> sum(shortlist)
6

>>> len(shortlist)
3

'''
Calculating the mean
'''
def calculate_mean(numbers):
    s = sum(numbers)
    N = len(numbers)
# Calculate the mean
    mean = s/N
    return mean


if __name__ == '__main__':
    donations = [100, 60, 70, 900, 100, 200, 500, 500, 503, 600, 1000, 1200]
    mean = calculate_mean(donations)
    N = len(donations)
    print('Mean donation over the last {0} days is {1}'.format(N, mean))

Finding the Median

samplelist = [4, 1, 3]
samplelist.sort()
samplelist
[1, 3, 4]

'''
Calculating the median
'''
def calculate_median(numbers):
    N = len(numbers)
    numbers.sort()
    # Find the median
    if N % 2 == 0:
        # if N is even
        m1 = N/2
        m2 = (N/2) + 1
        # Convert to integer, match position
        m1 = int(m1) - 1
        m2 = int(m2) - 1
        median = (numbers[m1] + numbers[m2])/2
    else:
        m = (N+1)/2
        # Convert to integer, match position
        m = int(m) - 1
        median = numbers[m]
    return median

if __name__ == '__main__':
    donations = [100, 60, 70, 900, 100, 200, 500, 500, 503, 600, 1000, 1200]
    median = calculate_median(donations)
    N = len(donations)
    print('Median donation over the last {0} days is {1}'.format(N, median))

Finding the Mode and Creating a Frequency Table

Finding the Most Common Elements

>>> simplelist = [4, 2, 1, 3, 4]
>>> from collections import Counter
>>> c = Counter(simplelist)
>>> c.most_common()
[(4, 2), (1, 1), (2, 1), (3, 1)]

>>> c.most_common(1)
[(4, 2)]

>>> c.most_common(2)
[(4, 2), (1, 1)]

>>> mode = c.most_common(1)
>>> mode
[(4, 2)]
v >>> mode[0]
(4, 2)
w >>> mode[0][0]
4

Finding the Mode

'''
Calculating the mode
'''
from collections import Counter
def calculate_mode(numbers):
    c = Counter(numbers)
    mode = c.most_common(1)
    return mode[0][0]
if __name__=='__main__':
    scores = [7, 8, 9, 2, 10, 9, 9, 9, 9, 4, 5, 6, 1, 5, 6, 7, 8, 6, 1, 10]
    mode = calculate_mode(scores)
    print('The mode of the list of numbers is: {0}'.format(mode))


'''
Calculating the mode when the list of numbers may
have multiple modes
'''
from collections import Counter
def calculate_mode(numbers):
    c = Counter(numbers)
    numbers_freq = c.most_common()
    max_count = numbers_freq[0][1]
    modes = []
    for num in numbers_freq:
        if num[1] == max_count:
            modes.append(num[0])
    return modes
if __name__ == '__main__':
    scores = [5, 5, 5, 4, 4, 4, 9, 1, 3]
    modes = calculate_mode(scores)
    print('The mode(s) of the list of numbers are:')
    for mode in modes:
        print(mode)

Creating a Frequency Table

'''
Frequency table for a list of numbers
'''
from collections import Counter

def frequency_table(numbers):
    table = Counter(numbers)
    print('Number\tFrequency')
    for number in table.most_common():
        print('{0}\t{1}'.format(number[0], number[1]))

if __name__=='__main__':
    scores = [7, 8, 9, 2, 10, 9, 9, 9, 9, 4, 5, 6, 1, 5, 6, 7, 8, 6, 1, 10]
    frequency_table(scores)



'''
Frequency table for a list of numbers
Enhanced to display the table sorted by the numbers
'''
from collections import Counter
def frequency_table(numbers):
    table = Counter(numbers)
    numbers_freq = table.most_common()
    numbers_freq.sort()
    print('Number\tFrequency')
    for number in numbers_freq:
        print('{0}\t{1}'.format(number[0], number[1]))

if __name__ == '__main__':
    scores = [7, 8, 9, 2, 10, 9, 9, 9, 9, 4, 5, 6, 1, 5, 6, 7, 8, 6, 1, 10]
    frequency_table(scores)

Measuring the Dispersion

Finding the Range of a Set of Numbers

'''
Find the range
'''
def find_range(numbers):
    lowest = min(numbers)
    highest = max(numbers)
    # Find the range
    r = highest-lowest
    return lowest, highest, r
if __name__ == '__main__':
    donations = [100, 60, 70, 900, 100, 200, 500, 500, 503, 600, 1000, 1200]
    lowest, highest, r = find_range(donations)
    print('Lowest: {0} Highest: {1} Range: {2}'.format(lowest, highest, r))

Finding the Variance and Standard Deviation

'''
Find the variance and standard deviation of a list of numbers
'''
def calculate_mean(numbers):
    s = sum(numbers)
    N = len(numbers)
    # Calculate the mean
    mean = s/N
    return mean
def find_differences(numbers):
    # Find the mean
    mean = calculate_mean(numbers)
    # Find the differences from the mean
    diff = []

    for num in numbers:
        diff.append(num-mean)
    return diff

    def calculate_variance(numbers):
        # Find the list of differences
        diff = find_differences(numbers)
        # Find the squared differences
        squared_diff = []
        for d in diff:
            squared_diff.append(d**2)
        # Find the variance
        sum_squared_diff = sum(squared_diff)
        variance = sum_squared_diff/len(numbers)
        return variance

if __name__ == '__main__':
    donations = [100, 60, 70, 900, 100, 200, 500, 500, 503, 600, 1000, 1200]
    variance = calculate_variance(donations)
    print('The variance of the list of numbers is {0}'.format(variance))
    std = variance**0.5
    print('The standard deviation of the list of numbers is {0}'.format(std))

Calculating the Correlation Between Two Data Sets

def find_corr_x_y(x,y):
    n = len(x)
    # Find the sum of the products
    prod = []
    for xi,yi in zip(x,y):
        prod.append(xi*yi)
    sum_prod_x_y = sum(prod)
    sum_x = sum(x)
    sum_y = sum(y)
    squared_sum_x = sum_x**2
    squared_sum_y = sum_y**2
    x_square = []
    for xi in x:
        x_square.append(xi**2)
    # Find the sum
    x_square_sum = sum(x_square)
    y_square=[]
    for yi in y:
        y_square.append(yi**2)
    # Find the sum
    y_square_sum = sum(y_square)

    # Use formula to calculate correlation
    numerator = n*sum_prod_x_y - sum_x*sum_y
    denominator_term1 = n*x_square_sum - squared_sum_x
    denominator_term2 = n*y_square_sum - squared_sum_y
    denominator = (denominator_term1*denominator_term2)**0.5
    correlation = numerator/denominator
    return correlation

High School Grades and Performance on College Admission Tests

Reading Data from Files

# Find the sum of numbers stored in a file
def sum_data(filename):
    s = 0
    with open(filename) as f:
        for line in f:
            s = s + float(line)
        print('Sum of the numbers: {0}'.format(s))
if __name__ == '__main__':
    sum_data('mydata.txt')


'''
Calculating the mean of numbers stored in a file
'''
def read_data(filename):
    numbers = []
    with open(filename) as f:
        for line in f:
            numbers.append(float(line))
    return numbers
def calculate_mean(numbers):
    s = sum(numbers)
    N = len(numbers)
    mean = s/N
    return mean
if __name__ == '__main__':
    data = read_data('mydata.txt')
    mean = calculate_mean(data)
    print('Mean: {0}'.format(mean))

Reading Data from a CSV File

import csv
import matplotlib.pyplot as plt
def scatter_plot(x, y):
    plt.scatter(x, y)
    plt.xlabel('Number')
    plt.ylabel('Square')
    plt.show()
def read_csv(filename):
    numbers = []
    squared = []
    with open(filename) as f:
        reader = csv.reader(f)
        next(reader)
        for row in reader:
            numbers.append(int(row[0]))
            squared.append(int(row[1]))
        return numbers, squared
if __name__ == '__main__':
    numbers, squared = read_csv('numbers.csv')
    scatter_plot(numbers, squared)