Average of even numbers till a given even number?

To find the average of even numbers till a given even number, we need to sum all the even numbers up to that number and divide by the count of even numbers.

Syntax

average = sum_of_even_numbers / count_of_even_numbers

Example

Average of even numbers till 10 is calculated as −

Even numbers: 2, 4, 6, 8, 10
Sum: 2 + 4 + 6 + 8 + 10 = 30
Count: 5
Average: 30 ÷ 5 = 6

There are two methods for calculating the average of even numbers till n (where n is even) −

• Using Loops − Iterate and sum all even numbers
• Using Formula − Apply mathematical formula (n+2)/2

Method 1: Using Loops

This approach iterates through all numbers from 1 to n, identifies even numbers, calculates their sum and count, then computes the average −

#include <stdio.h>

int main() {
    int n = 14, count = 0;
    float sum = 0;
    
    for (int i = 2; i <= n; i += 2) {
        sum = sum + i;
        count++;
    }
    
    float average = sum / count;
    printf("Even numbers till %d: ", n);
    for (int i = 2; i <= n; i += 2) {
        printf("%d ", i);
    }
    printf("\nSum: %.0f, Count: %d<br>", sum, count);
    printf("Average of even numbers till %d is %.2f<br>", n, average);
    
    return 0;
}

Even numbers till 14: 2 4 6 8 10 12 14 
Sum: 56, Count: 7
Average of even numbers till 14 is 8.00

Method 2: Using Formula

For even numbers till n (where n is even), the average can be calculated using the mathematical formula: (n + 2) / 2 −

#include <stdio.h>

int main() {
    int n = 14;
    
    if (n % 2 != 0) {
        printf("Please enter an even number.<br>");
        return 1;
    }
    
    float average = (float)(n + 2) / 2;
    printf("Using formula: (%d + 2) / 2 = %.2f<br>", n, average);
    printf("Average of even numbers till %d is %.2f<br>", n, average);
    
    return 0;
}

Using formula: (14 + 2) / 2 = 8.00
Average of even numbers till 14 is 8.00

Comparison

Conclusion

Both methods effectively calculate the average of even numbers. The formula method (n+2)/2 is more efficient for direct calculation, while the loop method provides better understanding of the underlying process.