python 分位数的差异（numpy，统计）

Question

今天我做了自己的函数来解决分位数/十分位数/百分位数：

from math import floor, ceil
def mean(x: list)->float:
""""arithmetic mean (average) of list
adding all elements and divide by umber of elements"""
if len(x) < 1:
    raise TypeError("mean need at least one element")
else:
    sum_of_elements =sum(x)
    mean_value = sum_of_elements/len(x)
    return mean_value

def percentiles(percentile, x:list)->float:
'''Percentile is the value below which the values of a given percentage of samples fall.
percentile = 25, 50, 75,100 is 1st, 2nd, 3rd and 4th quartile
percentile = 10,20,30,40,50,60,70,80,90,100 is 1st, 2nd, 3rd
4th, 5th, 6th, 7th, 8th, 9th and 10th decile.'''
x = sorted(x)
n = len(x)
if percentile <1 or percentile >100:
    raise TypeError("percentile should be in range 1-100")
if n<0:
    raise TypeError("list cannot be empty")
location = percentile*(n+1)/100
if int(location) == location:
    return x[int(location)-1]
else:
    down = floor(location)
    up = ceil(location)
    if down == 0:
        return x[up]
    else:
        even = mean([x[down-1], x[up-1]])
        return even

当我将上面的函数与 np.quantile 和 stats.quantiles 进行比较时，我得到了不同的结果。例如列表：[1,2,3,4,5,6,7,8,10,11,12,15,16,21] 我的第一季度：3.5 统计 q1：3.75（方法 = '排除'）或 4.25（方法 = '包含'） Numpy q1：4.25（？）

我的percentiles() 函数有什么问题？当我在纸上做时，我总是得到与百分位数（）相同的结果。

Answer 1

计算百分位数的正确公式应使用

(n-1)*percentile/100

作为乘数。这是更正后的

percentiles

函数：

from math import floor, ceil

def percentiles(percentile, x:list)->float:
    '''Percentile is the value below which the values of a given percentage of samples fall.
    percentile = 25, 50, 75, 100 is 1st, 2nd, 3rd and 4th quartile
    percentile = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 is 1st, 2nd, 3rd
    4th, 5th, 6th, 7th, 8th, 9th and 10th decile.'''
    x = sorted(x)
    n = len(x)
    
    if percentile < 1 or percentile > 100:
        raise ValueError("percentile should be in the range 1-100")
    if n < 1:
        raise ValueError("list cannot be empty")
    
    location = (n - 1) * percentile / 100  # Corrected formula
    
    if int(location) == location:
        return x[int(location)]
    else:
        down = floor(location)
        up = ceil(location)
        even = (x[down] + x[up]) / 2
        return even