中位数

将多个样本按照大小排序，取中间位置的元素。

若样本数量为奇数，中位数为最中间的元素

1 2000 3000 4000 10000000

若样本数量为偶数，中位数为最中间的两个元素的平均值

1 2000 3000 4000 5000 10000000

 

案例：分析中位数的算法，测试numpy提供的中位数API：

import numpy as np
closing_prices = np.loadtxt( '../../data/aapl.csv', 
    delimiter=',', usecols=(6), unpack=True)
size = closing_prices.size
sorted_prices = np.msort(closing_prices)
median = (sorted_prices[int((size - 1) / 2)] + sorted_prices[int(size / 2)]) / 2
print(median)
median = np.median(closing_prices)
print(median)

#中位数
import numpy as np
import matplotlib.pyplot as mp
import datetime as dt
import matplotlib.dates as md


def dmy2ymd(dmy):
  """
  把日月年转年月日
  :param day:
  :return:
  """
  dmy = str(dmy, encoding='utf-8')
  t = dt.datetime.strptime(dmy, '%d-%m-%Y')
  s = t.date().strftime('%Y-%m-%d')
  return s


dates, opening_prices, 
highest_prices, lowest_prices, 
closing_prices ,volumes= 
  np.loadtxt('aapl.csv',
             delimiter=',',
             usecols=(1, 3, 4, 5, 6,7),
             unpack=True,
             dtype='M8[D],f8,f8,f8,f8,f8',
             converters={1: dmy2ymd})  # 日月年转年月日




# 绘制收盘价的折现图
mp.figure('APPL', facecolor='lightgray')
mp.title('APPL', fontsize=18)
mp.xlabel('Date', fontsize=14)
mp.ylabel('Price', fontsize=14)
mp.grid(linestyle=":")

# 设置刻度定位器
# 每周一一个主刻度,一天一个次刻度

ax = mp.gca()
ma_loc = md.WeekdayLocator(byweekday=md.MO)
ax.xaxis.set_major_locator(ma_loc)
ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))
ax.xaxis.set_minor_locator(md.DayLocator())
# 修改dates的dtype为md.datetime.datetiem
dates = dates.astype(md.datetime.datetime)
mp.plot(dates, closing_prices,
                  color='dodgerblue',
                  linewidth=2,
                  linestyle='--',
                  alpha=0.8,
                  label='APPL Closing Price')


#中位数
# median = np.median(closing_prices)
sorted_prices = np.msort(closing_prices)
size = sorted_prices.size
median =(sorted_prices[int(size/2)]+sorted_prices[int((size-1)/2)])/2
print(median)#352.055
mp.hlines(median,dates[0],dates[-1],color='gold',label='median')
mp.legend()
mp.gcf().autofmt_xdate()
mp.show()