标准差计算公式_标准差的计算公式

1.计算公式

总体：

样本：

2.python算法案例

2.1 借助numpy计算

总体：

import numpy as np
data1 = [25,15,13,26,31,17,16,4,41,12]
data2 = [18,17,23,25,12,27,26,25,22,11]
data3 = [7,18,12,9,32,29,21,22,13,14]
print(np.std(data1), np.std(data2), np.std(data3))

10.207840124139876 5.499090833947008 7.874642849044012

样本：

import numpy as np
data1 = [25,15,13,26,31,17,16,4,41,12]
data2 = [18,17,23,25,12,27,26,25,22,11]
data3 = [7,18,12,9,32,29,21,22,13,14]
print(np.std(data1,ddof=1), np.std(data2,ddof=1), np.std(data3,ddof=1))

10.760008261045982 5.796550698475775 8.300602387778852

2.2 按基础算

总体：

data1 = [25,15,13,26,31,17,16,4,41,12]
data2 = [18,17,23,25,12,27,26,25,22,11]
data3 = [7,18,12,9,32,29,21,22,13,14]
# 求平均值
avg1 = sum(data1)/len(data1)
avg2 = sum(data2)/len(data2)
avg3 = sum(data3)/len(data3)
data11 = list(map(lambda x: x - avg1, data1))
data22 = list(map(lambda x: x - avg2, data2))
data33 = list(map(lambda x: x - avg3, data3))
data111 = list(map(lambda x: x**2, data11 ))
data222 = list(map(lambda x: x**2, data22 ))
data333 = list(map(lambda x: x**2, data22 ))
c1 = math.sqrt(sum(data111 )/len(data1))
c2 = math.sqrt(sum(data222 )/len(data2))
c3 = math.sqrt(sum(data333 )/len(data3))
print(c1, c2, c3)

10.207840124139876 5.499090833947008 7.874642849044013

样本：

data1 = [25,15,13,26,31,17,16,4,41,12]
data2 = [18,17,23,25,12,27,26,25,22,11]
data3 = [7,18,12,9,32,29,21,22,13,14]
# 求平均值
avg1 = sum(data1)/len(data1)
avg2 = sum(data2)/len(data2)
avg3 = sum(data3)/len(data3)
data11 = list(map(lambda x: x - avg1, data1))
data22 = list(map(lambda x: x - avg2, data2))
data33 = list(map(lambda x: x - avg3, data3))
data111 = list(map(lambda x: x**2, data11 ))
data222 = list(map(lambda x: x**2, data22 ))
data333 = list(map(lambda x: x**2, data33 ))
c1 = math.sqrt(sum(data111 )/(len(data1)-1))
c2 = math.sqrt(sum(data222 )/(len(data2)-1))
c3 = math.sqrt(sum(data333 )/(len(data3)-1))
print(c1, c2, c3)

10.760008261045982 5.796550698475775 8.300602387778854

2.3 其他

import numpy as np
np.mean() # 可以用来求平均值
np.sum() # 可以用来求和