Python Program to Find Median of a List

To find the median of a list in Python, sort the list and use median = sorted_list[len(sorted_list)//2] for odd length or average the two middle values for even length.

Examples

Input[3, 1, 2]

Output2

Input[4, 1, 7, 2]

Output3.0

Input[5]

Output5

How to Think About It

To find the median, first arrange the numbers in order from smallest to largest. If the list has an odd number of items, the median is the middle number. If it has an even number, the median is the average of the two middle numbers.

Algorithm

1

Sort the list in ascending order.

2

Check if the number of elements is odd or even.

3

If odd, return the middle element.

4

If even, return the average of the two middle elements.

Code

python

def find_median(numbers):
    sorted_list = sorted(numbers)
    n = len(sorted_list)
    mid = n // 2
    if n % 2 == 1:
        return sorted_list[mid]
    else:
        return (sorted_list[mid - 1] + sorted_list[mid]) / 2

# Example usage
print(find_median([3, 1, 2]))  # Output: 2
print(find_median([4, 1, 7, 2]))  # Output: 3.0

Output

2
3.0

Dry Run

Let's trace the list [4, 1, 7, 2] through the code

1

Sort the list

sorted_list = [1, 2, 4, 7]

2

Calculate length and middle index

n = 4, mid = 2

3

Check if length is odd or even

4 is even, so calculate average of sorted_list[1] and sorted_list[2]

4

Calculate median

median = (2 + 4) / 2 = 3.0

Step	Sorted List	n	mid	Median Calculation
1	[1, 2, 4, 7]	4	2	N/A
2	[1, 2, 4, 7]	4	2	N/A
3	[1, 2, 4, 7]	4	2	Average of 2 and 4
4	[1, 2, 4, 7]	4	2	3.0

Why This Works

Step 1: Sorting the list

Sorting arranges the numbers so the middle value(s) can be found easily.

Step 2: Finding the middle index

Dividing the length by 2 gives the middle position in the sorted list.

Step 3: Odd or even length check

If the list length is odd, the middle element is the median; if even, the median is the average of the two middle elements.

Alternative Approaches

Using statistics module

python

import statistics

def find_median(numbers):
    return statistics.median(numbers)

print(find_median([3, 1, 2]))  # Output: 2
print(find_median([4, 1, 7, 2]))  # Output: 3.0

This method is simpler and uses built-in functions but requires importing a module.

Manual sorting with bubble sort

python

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        for j in range(0, n - i - 1):
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
    return arr

def find_median(numbers):
    sorted_list = bubble_sort(numbers.copy())
    n = len(sorted_list)
    mid = n // 2
    if n % 2 == 1:
        return sorted_list[mid]
    else:
        return (sorted_list[mid - 1] + sorted_list[mid]) / 2

print(find_median([3, 1, 2]))  # Output: 2

This shows how to sort manually but is less efficient and more complex.

Complexity: O(n log n) time, O(n) space

Time Complexity

Sorting the list takes O(n log n) time, which dominates the median calculation.

Space Complexity

Sorting creates a new list, so space complexity is O(n). In-place sorting can reduce this.

Which Approach is Fastest?

Using the built-in statistics.median is fastest and simplest for most cases.

Approach	Time	Space	Best For
Manual sort + median	O(n log n)	O(n)	Learning sorting and median logic
statistics.median	O(n log n)	O(n)	Quick and reliable median calculation
Manual bubble sort + median	O(n^2)	O(n)	Understanding sorting basics, not efficient