Lower Median

The lower median of a dataset is the middle value when the set is sorted, assuming an odd number of elements. In the case of an even number of elements, the lower median is the smaller of the two middle numbers. Lower median is used in statistics as a measure of central tendency and can be used to divide a dataset into two equal parts. It provides insight into the central value of the dataset without being affected by outliers.

Java Code for Lower Median

In Java, you can find the lower median by first sorting the array and then selecting the middle element:

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import java.util.Arrays;

public class LowerMedian {
    public static int findLowerMedian(int[] arr) {
        Arrays.sort(arr);
        int n = arr.length;
        
        if (n % 2 != 0) {
            return arr[n / 2];
        } else {
            return arr[(n / 2) - 1];
        }
    }

    public static void main(String[] args) {
        int[] array = {5, 3, 9, 1, 4};
        int lowerMedian = findLowerMedian(array);
        System.out.println("The lower median is: " + lowerMedian);
    }
}

1. Sort the array using Arrays.sort.
2. If the array has an odd number of elements, return the middle one.
3. If the array has an even number of elements, return the smaller of the two middle ones.

C++ Code for Lower Median

In C++, similar to Java, you can find the lower median after sorting:

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#include <iostream>
#include <algorithm>

int findLowerMedian(int arr[], int size) {
    std::sort(arr, arr + size);
    if (size % 2 != 0) {
        return arr[size / 2];
    } else {
        return arr[(size / 2) - 1];
    }
}

int main() {
    int arr[] = {5, 3, 9, 1, 4};
    int lowerMedian = findLowerMedian(arr, 5);
    std::cout << "The lower median is: " << lowerMedian << std::endl;
}

1. Sort the array using std::sort.
2. Choose the middle element or the smaller of the two middle elements, based on the number of elements.

Python Code for Lower Median

Python also allows for a simple computation of the lower median:

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def find_lower_median(arr):
    arr.sort()
    n = len(arr)
    
    if n % 2 != 0:
        return arr[n // 2]
    else:
        return arr[(n // 2) - 1]

if __name__ == "__main__":
    arr = [5, 3, 9, 1, 4]
    lower_median = find_lower_median(arr)
    print(f"The lower median is: {lower_median}")

1. Sort the list using the built-in sort method.
2. Choose the middle element based on whether the list length is odd or even.

The implementations in Java, C++, and Python demonstrate how to find the lower median of an integer set. The key steps involve sorting the dataset and then selecting the middle value based on the dataset’s size.