Python分位數的計算

案例1

Ex1： Given a data = [6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36]，求Q1（25分位）, Q2（50分位）, Q3（75分位）, IQR
Solving：
步驟：
1. 排序，從小到大排列data，data = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
2. 計算分位數的位置
3. 給出分位數

分位數計算法一

pos = (n+1)*p，n爲數據的總個數，p爲0-1之間的值
Q1的pos = (11 + 1)*0.25 = 3 (p=0.25)      Q1=15
Q2的pos = (11 + 1)*0.5 = 6 (p=0.5)          Q2=40
Q3的pos = (11 + 1)*0.75 = 9 (p=0.75)     Q3=43
IQR = Q3 - Q1 = 28

import math
def quantile_p(data, p):
    pos = (len(data) + 1)*p
    #pos = 1 + (len(data)-1)*p
    pos_integer = int(math.modf(pos)[1])
    pos_decimal = pos - pos_integer
    Q = data[pos_integer - 1] + (data[pos_integer] - data[pos_integer - 1])*pos_decimal
    return Q

data = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
Q1 = quantile_p(data, 0.25)
print("Q1:", Q1)
Q2 = quantile_p(data, 0.5)
print("Q2:", Q2)
Q3 = quantile_p(data, 0.75)
print("Q3:", Q3)

分位數計算法二

pos = 1+ (n-1)*p，n爲數據的總個數，p爲0-1之間的值
Q1的pos = 1 + (11 - 1)*0.25 = 3.5 (p=0.25)      Q1=25.5
Q2的pos = 1 + (11 - 1)*0.5 = 6 (p=0.5)             Q2=40
Q3的pos = 1 + (11 - 1)*0.75 = 8.5 (p=0.75)     Q3=42.5

import math
def quantile_p(data, p):
    pos = 1 + (len(data)-1)*p
    pos_integer = int(math.modf(pos)[1])
    pos_decimal = pos - pos_integer
    Q = data[pos_integer - 1] + (data[pos_integer] - data[pos_integer - 1])*pos_decimal
    return Q
data = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
Q1 = quantile_p(data, 0.25)
print("Q1:", Q1)
Q2 = quantile_p(data, 0.5)
print("Q2:", Q2)
Q3 = quantile_p(data, 0.75)
print("Q3:", Q3)

 

概括總結

自定義分位數python代碼程序

import math
def quantile_p(data, p, method=1):
    data.sort()
    if method == 2:
        pos = 1 + (len(data)-1)*p
    else:
        pos = (len(data) + 1)*p
    pos_integer = int(math.modf(pos)[1])
    pos_decimal = pos - pos_integer
    Q = data[pos_integer - 1] + (data[pos_integer] - data[pos_integer - 1])*pos_decimal
    Q1 = quantile_p(data, 0.25)
    Q2 = quantile_p(data, 0.5)
    Q3 = quantile_p(data, 0.75)
    IQR = Q3 - Q1
    return Q1, Q2, Q3, IQR

 

pandas中的分位數程序

Python中可以利用Numpy庫來計算分位數，示例如下：

    import numpy as np
    a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
    # 中位數
    print(np.median(a))
    # 25%分位數
    print(np.percentile(a, 25))
    # 75%分位數
    print(np.percentile(a, 75))