使用 NumPy 在Python中计算平均值、方差和标准差

麻木的 在Python中是一个通用的数组处理包。它提供了一个高性能的多维数组对象和用于处理这些数组的工具。它是使用Python进行科学计算的基础包。 Numpy 提供了非常简单的方法来计算平均值、方差和标准差。

平均的

平均表示一组数据中的中心值或典型值的数字，特别是众数、中位数或（最常见的）平均值，其计算方法是将集合中值的总和除以它们的数字。 n 个数 x ₁ , x ₂ , ……x _n的平均值的基本公式是

$A = (x_1 + x_2 ........ + x_n)/ n$

例子：

假设有 8 个数据点，

$2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9$

这8个数据点的平均值是，

$A = \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5$

使用 Numpy 在Python中的平均值：

可以使用Python中的numpy.average()函数计算平均值。

Syntax: 

numpy.average(a, axis=None, weights=None, returned=False)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

weights: An array of weights associated with the values in a

returned: Default is False. If True, the tuple is returned, otherwise only the average is returned

示例 1：

Python

# Python program to get average of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [2, 4, 4, 4, 5, 5, 7, 9]
 
# Calculating average using average()
print(np.average(list))

输出：

5.0

示例 2：

Python

# Python program to get average of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [2, 40, 2, 502, 177, 7, 9]
 
# Calculating average using average()
print(np.average(list))

输出：

105.57142857142857

方差

方差是所有数字和平均值之间差异的平方和。方差的数学公式如下，

$Formula: \sigma^{2}= \frac { \sum_{i=1}^{N} (x_{i}-\mu)^{2}}{N}$

Where,

 ? is Mean, 

N is the total number of elements or frequency of distribution. 

例子：

让我们考虑我们平均采用的相同数据集。首先，计算每个数据点与平均值的偏差，并对每个结果求平方，

$\begin{array}{lll} (2-5)^2 = (-3)^2 = 9 && (5-5)^2 = 0^2 = 0 \\ (4-5)^2 = (-1)^2 = 1 && (5-5)^2 = 0^2 = 0 \\ (4-5)^2 = (-1)^2 = 1 && (7-5)^2 = 2^2 = 4 \\ (4-5)^2 = (-1)^2 = 1 && (9-5)^2 = 4^2 = 16. \\ \end{array}$
$variance = \frac{9 + 1 + 1 + 1 + 0 + 0 + 4 + 16}{8} = 4$

使用 Numpy 在Python中的差异：

可以使用Python中的numpy.var()函数计算方差。

Syntax: 

numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

dtype: Type to use in computing the variance. 

out: Alternate output array in which to place the result.

ddof: Delta Degrees of Freedom

keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one

示例 1：

Python

# Python program to get variance of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [2, 4, 4, 4, 5, 5, 7, 9]
 
# Calculating variance using var()
print(np.var(list))

输出：

4.0

示例 2：

Python

# Python program to get variance of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [212, 231, 234, 564, 235]
 
# Calculating variance using var()
print(np.var(list))

输出：

18133.359999999997

标准差

标准偏差是方差的平方根。它衡量数据与平均值的差异程度。计算标准差的数学公式如下，

$Standard Deviation = \sqrt{ variance }$

例子：

上述数据的标准差，

$Standard Deviation = \sqrt{ 4 } = 2$

使用 Numpy 在Python中的标准偏差：

可以使用Python中的numpy.std()函数计算标准偏差。

Syntax: 

numpy.std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

dtype: Type to use in computing the variance. 

out: Alternate output array in which to place the result.

ddof: Delta Degrees of Freedom

keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one

示例 1：

Python

# Python program to get
# standard deviation of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [2, 4, 4, 4, 5, 5, 7, 9]
 
# Calculating standard
# deviation using var()
print(np.std(list))

输出：

2.0

示例 2：

Python

# Python program to get
# standard deviation of a list
 
# Importing the NumPy module
import numpy as np
 
# Taking a list of elements
list = [290, 124, 127, 899]
 
# Calculating standard
# deviation using var()
print(np.std(list))

输出：

318.35750344541907