1.分位数计算案例
Ex1: Given a data = [6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36],求Q1, Q2, Q3, IQR
步骤:
1. 排序,从小到大排列data,data = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49]
2. 计算分位数的位置
3. 给出分位数
实例:
pos = (n+1)*p,n为数据的总个数,p为0-1之间的值
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
代码:
import math def quantile_p(data, p): 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 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)
计算方式二:
pos = 1+ (n-1)*p,n为数据的总个数,p为0-1之间的值
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
代码:
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)
示例2:
import math def quantile_p(data, p): data.sort() 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 return Q data = [7, 15, 36, 39, 40, 41] 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)
计算结果:
Q1 = 7 +(15-7)×(1.75 - 1)= 13
Q2 = 36 +(39-36)×(3.5 - 3)= 37.5
Q3 = 40 +(41-40)×(5.25 - 5)= 40.25
分位数计算法二:
结果:
Q1: 20.25
Q2: 37.5
Q3: 39.75
2. 分位数解释
概念:把给定的乱序数值由小到大排列并分成四等份,处于三个分割点位置的数值就是四分位数。
第1四分位数 (Q1),又称“较小四分位数”,等于该样本中所有数值由小到大排列后第25%的数字。
第2四分位数 (Q2),又称“中位数”,等于该样本中所有数值由小到大排列后第50%的数字。
第3四分位数 (Q3),又称“较大四分位数”,等于该样本中所有数值由小到大排列后第75%的数字。
四分位距(InterQuartile Range, IQR)= 第3四分位数与第1四分位数的差距
确定p分位数位置的两种方法
position = (n+1)*p
position = 1 + (n-1)*p
利用pandas求
import pandas as pd import numpy as np dt = pd.Series(np.array([6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36]) print("数据格式:") print(dt) print('Q1:', df.quantile(0.25)) print('Q2:', df.quantile(0.5)) print('Q3:', df.quantile(0.75))
3.去噪
import pandas as pd import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt import seaborn as sns #解决乱码和负值的负号不出现问题 mpl.rcParams['font.sans-serif'] = ['SimHei'] mpl.rcParams['axes.unicode_minus'] = False # 使显示图标自适应 mpl.rcParams['figure.autolayout'] = True #包装了一个异常值处理的代码,可以调用 def outliers_proc(data, col_name, scale=3): """ 用于清洗异常值,默认box_plot(scale=3)进行清洗 param data: 接收pandas数据格式 param col_name: pandas列名 param scale: 尺度 """ def box_plot_outliers(data_ser, box_scale): """ 利用箱线图去除异常值 :param data_ser: 接收 pandas.Series 数据格式 :param box_scale: 箱线图尺度 """ iqr = box_scale * (data_ser.quantile(0.75) - data_ser.quantile(0.25)) val_low = data_ser.quantile(0.25) - iqr val_up = data_ser.quantile(0.75) + iqr rule_low = (data_ser < val_low) rule_up = (data_ser > val_up) return (rule_low,rule_up),(val_low,val_up) data_n = data.copy() data_serier = data_n[col_name] rule, value = box_plot_outliers(data_serier,box_scale=scale) index = np.arange(data_serier.shape[0])[rule[0]|rule[1]] print("Delete number is:{}".format(len(index))) data_n = data_n.drop(index) data_n.reset_index(drop=True, inplace=True) print("Now column number is:{}".format(data_n.shape[0])) index_low = np.arange(data_serier.shape[0])[rule[0]] outliers = data_serier.iloc[index_low] print("Description of data less than the lower bound is:") print(pd.Series(outliers).describe()) index_up = np.arange(data_serier.shape[0])[rule[1]] outliers = data_serier.iloc[index_up] print("Description of data larger than the upper bound is:") print(pd.Series(outliers).describe()) fig, ax = plt.subplots(1,2, figsize=(10,7)) sns.boxplot(y=data[col_name],data=data,palette="Set1",ax=ax[0]) sns.boxplot(y=data_n[col_name],data=data_n,palette="Set1",ax=ax[1]) return data_n