在Python中如何找到列表的中值?列表可以是任意大小的,并且数字不保证是任何特定的顺序。

如果列表包含偶数个元素,则函数应返回中间两个元素的平均值。

以下是一些例子(为了便于展示,进行了排序):

median([1]) == 1
median([1, 1]) == 1
median([1, 1, 2, 4]) == 1.5
median([0, 2, 5, 6, 8, 9, 9]) == 6
median([0, 0, 0, 0, 4, 4, 6, 8]) == 2

当前回答

简单地说,创建一个中值函数,参数为数字列表,并调用该函数。

def median(l):
    l = sorted(l)
    lent = len(l)
    if (lent % 2) == 0:
        m = int(lent / 2)
        result = l[m]
    else:
        m = int(float(lent / 2) - 0.5)
        result = l[m]
    return result

其他回答

我为一组数字定义了一个中值函数

def median(numbers):
    return (sorted(numbers)[int(round((len(numbers) - 1) / 2.0))] + sorted(numbers)[int(round((len(numbers) - 1) // 2.0))]) / 2.0

sorted()函数对此非常有用。使用排序函数 要对列表排序,只需返回中间值(或两个中间值的平均值) 如果列表包含偶数个元素,则为。

def median(lst):
    sortedLst = sorted(lst)
    lstLen = len(lst)
    index = (lstLen - 1) // 2
   
    if (lstLen % 2):
        return sortedLst[index]
    else:
        return (sortedLst[index] + sortedLst[index + 1])/2.0

一个返回给定列表中值的简单函数:

def median(lst):
    lst = sorted(lst)  # Sort the list first
    if len(lst) % 2 == 0:  # Checking if the length is even
        # Applying formula which is sum of middle two divided by 2
        return (lst[len(lst) // 2] + lst[(len(lst) - 1) // 2]) / 2
    else:
        # If length is odd then get middle value
        return lst[len(lst) // 2]

一些关于中值函数的例子:

>>> median([9, 12, 20, 21, 34, 80])  # Even
20.5
>>> median([9, 12, 80, 21, 34])  # Odd
21

如果你想使用库,你可以简单地做:

>>> import statistics
>>> statistics.median([9, 12, 20, 21, 34, 80])  # Even
20.5
>>> statistics.median([9, 12, 80, 21, 34])  # Odd
21

我在“中位数的中位数”算法的Python实现中发布了我的解决方案,这比使用sort()稍微快一点。我的解决方案每列使用15个数字,速度~5N比每列使用5个数字的速度~10N快。最佳速度是~4N,但我可能是错的。

根据Tom在评论中的要求,我在这里添加了我的代码,以供参考。我认为速度的关键部分是每列使用15个数字,而不是5个。

#!/bin/pypy
#
# TH @stackoverflow, 2016-01-20, linear time "median of medians" algorithm
#
import sys, random


items_per_column = 15


def find_i_th_smallest( A, i ):
    t = len(A)
    if(t <= items_per_column):
        # if A is a small list with less than items_per_column items, then:
        #
        # 1. do sort on A
        # 2. find i-th smallest item of A
        #
        return sorted(A)[i]
    else:
        # 1. partition A into columns of k items each. k is odd, say 5.
        # 2. find the median of every column
        # 3. put all medians in a new list, say, B
        #
        B = [ find_i_th_smallest(k, (len(k) - 1)/2) for k in [A[j:(j + items_per_column)] for j in range(0,len(A),items_per_column)]]

        # 4. find M, the median of B
        #
        M = find_i_th_smallest(B, (len(B) - 1)/2)


        # 5. split A into 3 parts by M, { < M }, { == M }, and { > M }
        # 6. find which above set has A's i-th smallest, recursively.
        #
        P1 = [ j for j in A if j < M ]
        if(i < len(P1)):
            return find_i_th_smallest( P1, i)
        P3 = [ j for j in A if j > M ]
        L3 = len(P3)
        if(i < (t - L3)):
            return M
        return find_i_th_smallest( P3, i - (t - L3))


# How many numbers should be randomly generated for testing?
#
number_of_numbers = int(sys.argv[1])


# create a list of random positive integers
#
L = [ random.randint(0, number_of_numbers) for i in range(0, number_of_numbers) ]


# Show the original list
#
# print L


# This is for validation
#
# print sorted(L)[int((len(L) - 1)/2)]


# This is the result of the "median of medians" function.
# Its result should be the same as the above.
#
print find_i_th_smallest( L, (len(L) - 1) / 2)

Python 3.4有statistics.median:

返回数值数据的中位数(中间值)。 当数据点数为奇数时,返回中间的数据点。 当数据点数为偶数时,通过取两个中间值的平均值来插值中位数: >>>中位数([1,3,5]) 3. >>>中位数([1,3,5,7]) 4.0

用法:

import statistics

items = [6, 1, 8, 2, 3]

statistics.median(items)
#>>> 3

它对类型也非常小心:

statistics.median(map(float, items))
#>>> 3.0

from decimal import Decimal
statistics.median(map(Decimal, items))
#>>> Decimal('3')