findMedianNumbersRange()

Step 1: Understanding the problem

In this step, we need to understand the problem that we are trying to solve.

We want to create a function which computes the median of a range of numbers.

The median of a set of numbers is the middle number when the numbers are arranged in ascending order. If there are an even number of numbers, the median is the average of the two middle numbers.

This means we'll need a way to sort numbers in an array and then select the median value.

Let's start by creating the skeleton of our function.

function findMedianNumbersRange(numbers){
    // function will go here
}

Step 2: Validate the input

Before we deal with the actual logic of finding the median, we should check that our input meets the criteria that we expect. We expect to get an array of numbers. If the input is not an array, or if it's an empty array, we should return an error message.

Let's add this input validation now.

function findMedianNumbersRange(numbers){
    if (!Array.isArray(numbers) || numbers.length === 0) {
        return 'Invalid input. Please provide an array of numbers.';
    }
    // More function coding will go here later
}

Step 3: Sorting the array

Next, we need to sort the array of numbers in ascending order. JavaScript provides a built-in sort function that we can use. However, by default this function sorts numbers as if they were strings, which is not the behavior we would like. So we need to provide a custom compare function to the sort function.

function findMedianNumbersRange(numbers){
    if (!Array.isArray(numbers) || numbers.length === 0) {
        return 'Invalid input. Please provide an array of numbers.';
    }
    numbers.sort((a, b) => a - b);
    // We will continue function coding later
}

Step 4: Finding the median

Now that the numbers are sorted, we can go about finding the median.

If the length of the array is odd, the median is the number at the middle index.

If the length of the array is even, the median is the mean (i.e., average) of the two middle numbers.

To calculate this, we will first find the middle index using integer division (i.e., rounding down if necessary), then use this index to find the median.

function findMedianNumbersRange(numbers){
    if (!Array.isArray(numbers) || numbers.length === 0) {
        return 'Invalid input. Please provide an array of numbers.';
    }
    numbers.sort((a, b) => a - b);
    
    const midIndex = Math.floor(numbers.length / 2);
    
    let median;
    if (numbers.length % 2 === 0) { // If the array length is even
        median = (numbers[midIndex - 1] + numbers[midIndex]) / 2;
    } else { // If the array length is odd
        median = numbers[midIndex];
    }
    
    return median;
}

Conclusion

And there we have it! A function that correctly calculates the median of a range of numbers. This function should work for any array of numbers, and will return an error message if it finds anything but.