统计函数（Statistical Functions）

NumPy具有相当多的有用统计函数，用于从阵列中的给定元素中查找最小值，最大值，百分位数标准差和方差等。 功能说明如下 -

numpy.amin() and numpy.amax()

这些函数沿指定轴返回给定数组中元素的最小值和最大值。

例子 (Example)

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 
print 'Our array is:' 
print a  
print '\n'  
print 'Applying amin() function:' 
print np.amin(a,1) 
print '\n'  
print 'Applying amin() function again:' 
print np.amin(a,0) 
print '\n'  
print 'Applying amax() function:' 
print np.amax(a) 
print '\n'  
print 'Applying amax() function again:' 
print np.amax(a, axis = 0)

它将产生以下输出 -

Our array is:
[[3 7 5]
[8 4 3]
[2 4 9]]
Applying amin() function:
[3 3 2]
Applying amin() function again:
[2 4 3]
Applying amax() function:
9
Applying amax() function again:
[8 7 9]

numpy.ptp()

numpy.ptp()函数返回沿轴的值范围（最大值 - 最小值）。

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 
print 'Our array is:' 
print a 
print '\n'  
print 'Applying ptp() function:' 
print np.ptp(a) 
print '\n'  
print 'Applying ptp() function along axis 1:' 
print np.ptp(a, axis = 1) 
print '\n'   
print 'Applying ptp() function along axis 0:'
print np.ptp(a, axis = 0) 

它将产生以下输出 -

Our array is:
[[3 7 5]
[8 4 3]
[2 4 9]]
Applying ptp() function:
7
Applying ptp() function along axis 1:
[4 5 7]
Applying ptp() function along axis 0:
[6 3 6]

numpy.percentile()

百分位数（或百分位数）是统计中使用的度量，指示一组观察中给定百分比的观察值下降的值。 函数numpy.percentile()接受以下参数。

numpy.percentile(a, q, axis)

Where,

例子 (Example)

import numpy as np 
a = np.array([[30,40,70],[80,20,10],[50,90,60]]) 
print 'Our array is:' 
print a 
print '\n'  
print 'Applying percentile() function:' 
print np.percentile(a,50) 
print '\n'  
print 'Applying percentile() function along axis 1:' 
print np.percentile(a,50, axis = 1) 
print '\n'  
print 'Applying percentile() function along axis 0:' 
print np.percentile(a,50, axis = 0)

它将产生以下输出 -

Our array is:
[[30 40 70]
 [80 20 10]
 [50 90 60]]
Applying percentile() function:
50.0
Applying percentile() function along axis 1:
[ 40. 20. 60.]
Applying percentile() function along axis 0:
[ 50. 40. 60.]

numpy.median()

Median定义为将数据样本的较高一半与下半部分分开的值。 使用numpy.median()函数，如以下程序所示。

例子 (Example)

import numpy as np 
a = np.array([[30,65,70],[80,95,10],[50,90,60]]) 
print 'Our array is:' 
print a 
print '\n'  
print 'Applying median() function:' 
print np.median(a) 
print '\n'  
print 'Applying median() function along axis 0:' 
print np.median(a, axis = 0) 
print '\n'  
print 'Applying median() function along axis 1:' 
print np.median(a, axis = 1)

它将产生以下输出 -

Our array is:
[[30 65 70]
 [80 95 10]
 [50 90 60]]
Applying median() function:
65.0
Applying median() function along axis 0:
[ 50. 90. 60.]
Applying median() function along axis 1:
[ 65. 80. 60.]

numpy.mean()

算术平均值是沿轴的元素之和除以元素的数量。 numpy.mean()函数返回数组中元素的算术平均值。 如果提到轴，则沿着它计算。

例子 (Example)

import numpy as np 
a = np.array([[1,2,3],[3,4,5],[4,5,6]]) 
print 'Our array is:' 
print a 
print '\n'  
print 'Applying mean() function:' 
print np.mean(a) 
print '\n'  
print 'Applying mean() function along axis 0:' 
print np.mean(a, axis = 0) 
print '\n'  
print 'Applying mean() function along axis 1:' 
print np.mean(a, axis = 1)

它将产生以下输出 -

Our array is:
[[1 2 3]
 [3 4 5]
 [4 5 6]]
Applying mean() function:
3.66666666667
Applying mean() function along axis 0:
[ 2.66666667 3.66666667 4.66666667]
Applying mean() function along axis 1:
[ 2. 4. 5.]

numpy.average()

加权平均值是由每个分量乘以反映其重要性的因子得到的平均值。 numpy.average()函数根据另一个数组中给出的各自权重计算数组中元素的加权平均值。 该函数可以具有轴参数。 如果未指定轴，则数组将展平。

考虑阵列[1,2,3,4]和相应的权重[4,3,2,1]，通过将相应元素的乘积相加并将总和除以权重之和来计算加权平均值。

加权平均值=（1 * 4 + 2 * 3 + 3 * 2 + 4 * 1）/（4 + 3 + 2 + 1）

例子 (Example)

import numpy as np 
a = np.array([1,2,3,4]) 
print 'Our array is:' 
print a 
print '\n'  
print 'Applying average() function:' 
print np.average(a) 
print '\n'  
# this is same as mean when weight is not specified 
wts = np.array([4,3,2,1]) 
print 'Applying average() function again:' 
print np.average(a,weights = wts) 
print '\n'  
# Returns the sum of weights, if the returned parameter is set to True. 
print 'Sum of weights' 
print np.average([1,2,3, 4],weights = [4,3,2,1], returned = True)

它将产生以下输出 -

Our array is:
[1 2 3 4]
Applying average() function:
2.5
Applying average() function again:
2.0
Sum of weights
(2.0, 10.0)

在多维数组中，可以指定用于计算的轴。

例子 (Example)

import numpy as np 
a = np.arange(6).reshape(3,2) 
print 'Our array is:' 
print a 
print '\n'  
print 'Modified array:' 
wt = np.array([3,5]) 
print np.average(a, axis = 1, weights = wt) 
print '\n'  
print 'Modified array:' 
print np.average(a, axis = 1, weights = wt, returned = True)

它将产生以下输出 -

Our array is:
[[0 1]
 [2 3]
 [4 5]]
Modified array:
[ 0.625 2.625 4.625]
Modified array:
(array([ 0.625, 2.625, 4.625]), array([ 8., 8., 8.]))

标准偏差

标准偏差是平均偏差平均值的平方根。 标准差的公式如下 -

std = sqrt(mean(abs(x - x.mean())**2))

如果数组是[1,2,3,4]，那么它的平均值是2.5。 因此，平方偏差为[2.25,0.25,0.25,2.25]，其平均值的平方根除以4，即sqrt（5/4）为1.1180339887498949。

例子 (Example)

import numpy as np 
print np.std([1,2,3,4])

它将产生以下输出 -

1.1180339887498949 

Variance

方差是平方偏差的平均值，即mean(abs(x - x.mean())**2) 。 换句话说，标准差是方差的平方根。

例子 (Example)

import numpy as np 
print np.var([1,2,3,4])

它将产生以下输出 -

1.25