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
你能解释一下如何计算 3.25 和 7.75 的值吗？我预计他们是 3 和 8。
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
第 2 步：减去1以获得从第一个项目到最后一个项目的距离x
# n = (length - 1)
# n = (10-1)
# Output --> 9
第 3 步：乘以n分位数，这里是第 25 个百分位数或 0.25 个分位数或第一个四分位数
n * 0.25
# Therefore, (9 * 0.25)
# Output --> 2.25
# So, fraction is 0.25 part of 2.25
# m = 0.25
Step-4 : 现在得到最终答案
对于线性：
# 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
对于较低：
# 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
对于更高：
# 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
对于最近的：
# 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
对于中点：
# 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
There are various options that can be used depending on the type of interpolation method that you want the percentile to be calculated at.
a = np.arange(1, 11)
a # array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
np.percentile(a, (25, 75), interpolation='midpoint') # array([3.5, 7.5])
np.percentile(a, (25, 75), interpolation='nearest') # array([3, 8])
np.percentile(a, (25, 75), interpolation='nearest') # array([3, 8])
np.percentile(a, (25, 75), interpolation='linear') # array([3.25, 7.75])
np.percentile(a, (25, 75), interpolation='lower') # array([3, 7])
np.percentile(a, (25, 75), interpolation='higher') # array([4, 8])
You will note that the cumulative relative frequency is what the percentiles need to be derived from
c = np.cumsum(a)
c # ---- array([ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55], dtype=int32)
c/c[-1] * 100
array([ 1.81818182, 5.45454545, 10.90909091, 18.18181818,
27.27272727, 38.18181818, 50.90909091, 65.45454545,
81.81818182, 100. ])
and percentiles for 25 and 75 will require an interpolation of some form.
从numpy 文档：
给定一个长度为 N 的向量 V，V 的第 q 个百分位数是 V 的排序副本中从最小值到最大值的值 q/100。两个最近邻居的值和距离以及如果归一化排名与 q 的位置不完全匹配，插值参数将确定百分位数。如果 q=50，此函数与中位数相同，如果 q=0，则与最小值相同，如果 q=100，则与最大值相同。
所以问题在于当找不到与您的分位数完全匹配时 numpy 的反应。如果你使用interpolation="nearest"，你会得到你期望得到的结果：
>>> 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, interpolation="nearest")
>>> quartile_3 = percentile(data, 75, interpolation="nearest")
>>> print(quartile_1)
3
>>> print(quartile_3)
8