Data analysis (eight) standard deviation

Sample: S = [s1, s2, ..., sn]

Average: m = (s1 + s2 + ... + sn) / n

Dispersion: D = [d1, d2, ..., dn], di = si-m

Deviation side: Q = [q1, q2, ..., qn], qi = di ** 2

Variance: v = (q1 + q2 + ... + qn) / n

The overall standard deviation: s = sqrt (v), root mean square

Sample variance: v '= (q1 + q2 + ... + qn) / (n-1)

Sample standard deviation: s '= sqrt (v'), root mean square

np.std (Array)             # overall standard deviation 
np.std (Array, ddof =. 1)     # Sample standard deviation

 

# 中位数
import numpy as np
import datetime as dt



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 ), 
             the unpack = True, 
             DTYPE = ' M8 [D], F8, F8, F8, F8, F8 ' , 
             Converters = {. 1: dmy2ymd})   # DMY transfer date 
# overall standard deviation entertained 
std_c = np.std (closing_prices)
 Print (std_c)   # 7.080008325481608 
# overall standard deviation opening 
std_o = np.std (opening_prices)
 Print (std_o)   #7.099438350242144 

std_c2 = np.std (closing_prices, ddof =. 1)   # Sample standard deviation 
Print (std_c2)   # 7.201042876260849 
# implemented manually 
m = np.mean (closing_prices) # arithmetic mean 
D = closing_prices - m # spreads 
v = np. Mean (D ** 2) # deviation side 
S = np.sqrt (V) # population standard deviation 
Print (S)   # 7.080008325481608 
V2 = (D ** 2) .sum () / (d.size -. 1 ) 
S2 = np.sqrt (V2)
 Print (S2)   # sample standard deviation 
# 7.201042876260849