how-to-find-the-median-of-a-list-in-python

How to Find the Median of a List in Python

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Introduction

The Median is the value that lies in the center when the numbers are arranged in ascending order.

General steps to find Median in Mathematical problems:

1. First count the number of elements(N) that lie in your collection(list, tuple, set) and sort them in ascending order.

2. Check whether the number of elements is odd or even.

3. If the number of elements(N) is odd.

The median is the middle value, which is at position (N + 1)/2

4. If the number of elements(N) is even.

The median is the average of the two middle values.

a. Find the value at position (N/2)

b. Find the value at position (N/2) + 1

c. Find the average of the two values to get the median.

For example:

1. list_1 = [2, 4, 5, 8, 14]

Since N = 5 which is odd, the Median is the middle value that is 5
2. list_2 = [9, 3, 1, 8, 3, 6]

Here, N = 6 which is even.

Sort the list as: [1, 3, 3, 6, 8, 9]

Median = (3 + 6)/2 = 4.5

 

Python ways to find the Median

In Python, we can use different methods in order to find the median of the list. Here in the blog post, we are discussing three methods to calculate the median in the list and they are:

A. Using user-defined function

Despite using the library, we can make our own function that can calculate the median from the list simply by reflecting the above processes.

def calculate_median(nums):
    """function to calculate the median of the list"""
    print(f"The median of the list {nums} is", end=" ")

    # calculate length of list
    N = len(nums)

    # sort the list in ascending order
    nums.sort()

    mid_index = N // 2 # floor division // rounds the result down to the nearest whole number

    if N % 2 != 0:
        print(nums[mid_index])
    else:
        print((nums[mid_index - 1] + nums[mid_index]) / 2)


# list containing all unique items
calculate_median([7, 2, 1, 9, 4])
# list containing two or similar items
calculate_median([11, 7, 11, 18, 9, 7, 6, 23, 7])
# list containing floating point numbers
calculate_median([1.7, 3.4, 10.9, 4.2])

Output:

The median of the list [7, 2, 1, 9, 4] is 4
The median of the list [11, 7, 11, 18, 9, 7, 6, 23, 7] is 9
The median of the list [1.7, 3.4, 10.9, 4.2] is 3.8

 

B. Using Python built-in module named statistics

Statistics is the Python built-in module that provides functions for calculating mathematical statistics of numeric data.
This module includes functions that can calculate the arithmetic mean, geometric mean, harmonic mean, median, mode, quantiles, and many others.

from statistics import median


def calculate_median(nums):
    """function to calculate the median of the list 
        using Python statistics module"""
    print(f"The median of the list {nums} is", median(nums))


# list containing all unique items
calculate_median([33, 55, 77, 22, 11, 88, 44])
# list containing two or similar items
calculate_median([4, 12, 14, 17, 22, 23, 23, 24, 25, 29, 40, 67, 77, 82, 92])
# list containing floating point numbers
calculate_median([1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75])

Output:

The median of the list [33, 55, 77, 22, 11, 88, 44] is 44
The median of the list [4, 12, 14, 17, 22, 23, 23, 24, 25, 29, 40, 67, 77, 82, 92] is 24
The median of the list [1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75] is 1.84

Note: if you pass the empty list, then the statistics module raises StatisticsError.

.....
.....
.....

# calling function with the empty list
calculate_median([])

statistics_error_median_python

 

C. Using a third-party library called NumPy

NumPy is the third-party library for scientific computing in Python. It can be used to perform various mathematical operations on arrays.

We can simply install it using pip on a virtual environment as:

pip install numpy
import numpy as np


def calculate_median(nums):
    """function to calculate the median of the list 
        using third-party library NumPy"""
    print(f"The median of the list {nums} is", np.median(nums))


# list containing all unique items
calculate_median([34, 344, 12, 77, 45, 90])
# list containing two or similar items
calculate_median([1001, 777, 1001, 189, 189, 777, 6098, 23, 777])
# list containing floating point numbers
calculate_median([1.47, 56.84, 134.9, 565.2])
calculate_median([])

Output:

The median of the list [34, 344, 12, 77, 45, 90] is 61.0
The median of the list [1001, 777, 1001, 189, 189, 777, 6098, 23, 777] is 777.0
The median of the list [1.47, 56.84, 134.9, 565.2] is 95.87

 

Conclusion

So far we have discussed three methods for calculating the median of the list. Every method is suitable to use based on our use cases. For example, if you don’t want to depend on Python’s built-in module and a third-party one, you can create your own function and do some tweaks to get the formatted output you want.

References:
Statistics Module
NumPy

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