In [1]:
num_friends = [100,49,41,40,25,21,21,19,19,18,18,16,15,15,15,15,14,14,13,13,13,13,12,12,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
In [2]:
from collections import Counter
In [3]:
%matplotlib inline
from matplotlib import pyplot as plt
In [4]:
# Figure 5-1. A histogram of friend counts
friend_counts = Counter(num_friends)
xs = range(101)
ys = [friend_counts[x] for x in xs]
plt.bar(xs, ys)
plt.axis([0, 101, 0, 25])
plt.title("Histogram of Friend Counts")
plt.xlabel('# of friends')
plt.ylabel('# of people')
plt.show()
In [5]:
num_points = len(num_friends)
num_points
Out[5]:
In [6]:
largest_value = max(num_friends)
largest_value
Out[6]:
In [7]:
smallest_value = min(num_friends)
smallest_value
Out[7]:
In [8]:
sorted_values = sorted(num_friends)
In [9]:
smallest_value = sorted_values[0]
smallest_value
Out[9]:
In [10]:
second_smallest_value = sorted_values[1]
second_smallest_value
Out[10]:
In [11]:
second_largest_value = sorted_values[-2]
second_largest_value
Out[11]:
In [12]:
def mean(x):
return sum(x) / len(x)
In [13]:
mean(num_friends)
Out[13]:
In [14]:
def median(v):
"""finds the middle-most value"""
n = len(v)
sorted_v = sorted(v)
midpoint = n // 2
if n % 2 == 1:
# if odd, return the middle value
return sorted_v[midpoint]
else:
# if even, return the average of middle values
lo = midpoint - 1
hi = midpoint
return (sorted_v[lo] + sorted_v[hi]) / 2
In [15]:
median(num_friends)
Out[15]:
In [17]:
def quantile(x, p):
"""returns the pth-percentile value in x"""
p_index = int(p * len(x))
return sorted(x)[p_index]
In [18]:
quantile(num_friends, 0.10)
Out[18]:
In [19]:
quantile(num_friends, 0.25)
Out[19]:
In [20]:
quantile(num_friends, 0.70)
Out[20]:
In [22]:
quantile(num_friends, 0.90)
Out[22]:
In [23]:
def mode(x):
"""returns a list, might be more than one mode"""
counts = Counter(x)
max_count = max(counts.values())
return [x_i for x_i, count in counts.items() if count == max_count]
In [24]:
mode(num_friends)
Out[24]:
In [25]:
def data_range(x):
return max(x) - min(x)
In [26]:
data_range(num_friends)
Out[26]:
In [28]:
def de_mean(x):
"""translates x by substracting its mean"""
x_bar = mean(x)
return [x_i - x_bar for x_i in x]
In [29]:
def variance(x):
"""assume x has at least 2 elements"""
n = len(x)
deviation = de_mean(x)
return sum(dev ** 2 for dev in deviation) / (n - 1)
In [30]:
variance(num_friends)
Out[30]:
In [31]:
import math
In [32]:
def standard_deviation(x):
return math.sqrt(variance(x))
In [33]:
standard_deviation(num_friends)
Out[33]:
In [34]:
def interquartile_range(x):
return quantile(x, 0.75) - quantile(x, 0.25)
In [35]:
interquartile_range(num_friends)
Out[35]:
In [36]:
def covariance(x, y):
n = len(x)
return sum(x_i * y_i for x_i, y_i in zip(de_mean(x), de_mean(y))) / (n - 1)
In [37]:
daily_minutes = [1,68.77,51.25,52.08,38.36,44.54,57.13,51.4,41.42,31.22,34.76,54.01,38.79,47.59,49.1,27.66,41.03,36.73,48.65,28.12,46.62,35.57,32.98,35,26.07,23.77,39.73,40.57,31.65,31.21,36.32,20.45,21.93,26.02,27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,38.11,38.18,36.31,21.03,30.86,36.07,28.66,29.08,37.28,15.28,24.17,22.31,30.17,25.53,19.85,35.37,44.6,17.23,13.47,26.33,35.02,32.09,24.81,19.33,28.77,24.26,31.98,25.73,24.86,16.28,34.51,15.23,39.72,40.8,26.06,35.76,34.76,16.13,44.04,18.03,19.65,32.62,35.59,39.43,14.18,35.24,40.13,41.82,35.45,36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,26.89,23.48,8.38,27.81,32.35,23.84]
In [39]:
covariance(num_friends, daily_minutes)
Out[39]:
In [40]:
def correlation(x, y):
stdev_x = standard_deviation(x)
stdev_y = standard_deviation(y)
if stdev_x > 0 and stdev_y > 0:
return covariance(x, y) / (stdev_x * stdev_y)
else:
return 0
In [41]:
correlation(num_friends, daily_minutes)
Out[41]:
In [42]:
outlier = num_friends.index(100)
In [43]:
num_friends_good = [x
for i, x in enumerate(num_friends)
if i != outlier]
daily_minutes_good = [y
for i, y in enumerate(daily_minutes)
if i != outlier]
In [44]:
correlation(num_friends_good, daily_minutes_good)
Out[44]: