Finding the largest averaged array
First of all, a minor complaint, but be careful when using 'use strict'; at a file level—when concatenating JavaScript files for minification, this can have adverse affects. Whenever possible, use it at the top of a function instead.

Anyway, on to the actual code. Your arrayAverage function is fine, but it could be improved and made more explicit by using a more functional style. The .reduce function is perfect for this case, turning the function into a simple one-liner:

function arrayAverage(array) {
  return array.reduce(function (a, b) { return a + b; }) / array.length;
}


Your compare function is, frankly, rather odd. I see three main problems with it:


It does not handle arrays that have equal averages very well. Simply preferring the second array is not a good compromise.
Returning strings for the result is a little strange and unnatural. While there are no enums in a language like JavaScript, using string literals is not a good replacement.
The name compare is very generic and doesn't explain what the function does at all.


To fix all these problems, I propose the following function:

function arrayCompare(arrayA, arrayB) {
  var averageA = arrayAverage(arrayA),
      averageB = arrayAverage(arrayB);
  return averageA &lt; averageB ? -1
       : averageA &gt; averageB ?  1
                             :  0;
}


This is clearer, and it handles the equality case more elegantly. If you really hate nested conditional expressions with a passion, you could use a set of if statements instead, but I think this is perfectly readable when properly formatted.

This change eliminates the need for the largestAveragedArray function entirely, simplifying the code somewhat. As a final note, document.write makes me cringe, but I understand that it's useful in code snippets, so I'll let it slide here. Just don't use it in a real project.



(function () {
  'use strict';
  
  // returns the average of a single array
  function arrayAverage(array) {
    return array.reduce(function (a, b) { return a + b; }) / array.length;
  }
  
  // compares two arrays;
  // returns -1 if avg(a) &lt; avg(b), 1 if avg(a) &gt; avg(b), or 0 if avg(a) = avg(b)
  function arrayCompare(arrayA, arrayB) {
    var averageA = arrayAverage(arrayA),
        averageB = arrayAverage(arrayB);
    return averageA &lt; averageB ? -1
         : averageA &gt; averageB ?  1
                               :  0;
  }

  var smaller = [100, 80],
      larger = [100, 100];
  
  document.write(arrayCompare(smaller, larger) + '&lt;br&gt;' + arrayCompare(larger, smaller) + '&lt;br&gt;' + arrayCompare(smaller, smaller));
})();