数据科学中的统计学

# -*- coding: utf-8 -*-"""Spyder EditorAThis is a temporary script file."""

from collections import Counterimport matplotlib.pyplot as plt

num_friends = [100, 55, 99, 24, 24, 55]

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, 5])plt.title("Histogram of Friend Counts")plt.xlabel("# of freinds")plt.ylabel("# of people")plt.show()

# -*- coding: utf-8 -*-"""Spyder EditorAThis is a temporary script file."""

from typing import List

def quantile(xs:List[float], p:float) -> float:p_index = int(p * len(xs))return sorted(xs)[p_index]

print(quantile([1, 3, 4, 1, 2], 0.25)) #1

# -*- coding: utf-8 -*-"""Spyder EditorAThis is a temporary script file."""

from typing import List,Counter

def mode(xs: List[float]) -> List[float]:"""因为众数可能有多个，所以需要返回一个列表"""counts = Counter(xs)max_counts = max(counts.values())return [x_i for x_i, count in counts.items() if count == max_counts]

print(mode([1,2,3,41,1,2])) #[1, 2]

# -*- coding: utf-8 -*-"""Spyder EditorAThis is a temporary script file."""

from typing import Listfrom statistics import meanimport math

def decline_mean(x: List[float]) -> List[float]:x_mean = mean(x)return [x_i - x_mean for x_i in x]

def sum_of_squares(x: List[float]) -> float:list_squares = [x_i * x_i for x_i in x]return sum(list_squares)

# 计算方差def variance(xs: List[float]) -> float:n = len(xs)deviations = decline_mean(xs)return sum_of_squares(deviations) / (n - 1)

# 计算标准差def standard_variance(xs: List[float]) -> float:return math.sqrt(variance(xs))

print(variance([1,2,3,4])) #1.6666666666666667 方差print(standard_variance([1,2,3,4])) #1.2909944487358056 标准差

# -*- coding: utf-8 -*-"""Spyder EditorAThis is a temporary script file."""

from typing import List

def quantile(xs: List[float], p: float) -> float:p_index = int(p * len(xs))return sorted(xs)[p_index]

def interquartile_range(xs: List[float]) -> float:return quantile(xs, 0.75) - quantile(xs, 0.25)

print(interquartile_range([1, 3, 4, 1, 2])) #2

from typing import Listfrom statistics import mean

Vector = List[float]

def covariance(xs: List[float], ys: List[float]) -> float:assert len(xs) == len(ys), "must have same number of elements"return dot(decline_mean(xs), decline_mean(ys)) / (len(xs) - 1)

def dot(v: Vector, w: Vector) -> Vector:# 判定长度是否相同assert len(v) == len(w), "vector have same length"return sum(v_i * w_i for v_i, w_i in zip(v, w))

def decline_mean(x: List[float]) -> List[float]:x_mean = mean(x)return [x_i - x_mean for x_i in x]

print(covariance([1,2], [2,3])) #0.5