使用Numpy，如何计算1号to10的25百分位数？

Question

from numpy import percentile
import numpy as np
data=np.array([1,2,3,4,5,6,7,8,9,10])
# calculate quartiles
quartile_1 = percentile(data, 25)
quartile_3 =percentile(data, 75)
# calculate min/max

print(quartile_1) # show 3.25
print(quartile_3) # shows 7.75

你能解释一下3.25和7.75的价值是如何计算的吗？我预计他们是3岁和8岁。

Answer 1

手动逐步计算Numpy百分位数：

第1步：查找长度

x = [1,2,3,4,5,6,7,8,9,10]
l = len(x) 
# Output --> 10

Step-2：减去1得到x中从第一项到最后一项的距离

# n = (length - 1) 
# n = (10-1) 
# Output --> 9

Step-3：将n乘以分位数，这里是第25个百分位数或0.25个分位数或1个四分位数

n * 0.25
# Therefore, (9 * 0.25) 
# Output --> 2.25
# So, fraction is 0.25 part of 2.25
# m = 0.25

第4步：现在获取最终答案

线性：

# i + (j - i) * m
# Here, think i and j as values at indices
# x = [1,2,3,4,5,6,7,8,9,10]
#idx= [0,1,2,3,.........,9]
# So, for '2.25':
# value at index immediately before 2.25, is at index=2 so, i=3
# value at index immediately after 2.25, is at index=3 so, i=4
# and fractions 
3 + (4 - 3)*0.25
# Output --> 3.25

针对较低的

# Here, based on output from Step-3
# Because, it is '2.25', 
# Find a number a index lower than 2.25
# So, lower index is '2'
# x = [1,2,3,4,5,6,7,8,9,10]
#idx= [0,1,2,3,.........,9]
# So, at index=2 we have '3' 
# Output --> 3

适用于更高的

# Here, based on output from Step-3
# Because, it is '2.25', 
# Find a number a index higher than 2.25
# So, higher index is '3'
# x = [1,2,3,4,5,6,7,8,9,10]
#idx= [0,1,2,3,.........,9]
# So, at index=3 we have '4' 
# Output --> 4

最近的

# Here, based on output from Step-3
# Because, it is '2.25', 
# Find a number a index nearest to 2.25
# So, nearest index is '2'
# x = [1,2,3,4,5,6,7,8,9,10]
#idx= [0,1,2,3,.........,9]
# So, at index=2 we have '3' 
# Output --> 3

适用于中点的

# Here, based on output from Step-3
# (i + j)/2
# Here, think i and j as values at indices
# x = [1,2,3,4,5,6,7,8,9,10]
#idx= [0,1,2,3,.........,9]
# So, for '2.25'
# value at index immediately before 2.25, is at index=2 so, i=3
# value at index immediately after 2.25, is at index=3 so, i=4
(3+4)/2
# Output --> 3.5

Python中的代码：

x = np.array([1,2,3,4,5,6,7,8,9,10])
print("linear:", np.percentile(x, 25, interpolation='linear'))
print("lower:", np.percentile(x, 25, interpolation='lower'))
print("higher:", np.percentile(x, 25, interpolation='higher'))
print("nearest:", np.percentile(x, 25, interpolation='nearest'))
print("midpoint:", np.percentile(x, 25, interpolation='midpoint'))

输出：

linear: 3.25
lower: 3
higher: 4
nearest: 3
midpoint: 3.5

Answer 2

1.9.0版或更高版本的Numpy有一个可选的'interpolation‘参数，默认情况下是线性的。

此可选参数指定当所需的百分位数位于两个数据点i‘线性’：i+ (j - i) *分数，其中分数是由i和j包围的索引的分数部分。

如果要更改该行为，只需手动添加参数并使用interpolation='nearest’覆盖默认值

Answer 3

虽然这可能是一个插值问题，但通过某些方法(即方法2)，答案应该是[3, 8]

根据我的答案here和here，numpy使用方法3。

不幸的是，除非统计领域对四分位数有一个统一的定义，否则混乱将会继续下去。