How to change AngularJS data outside the scope?

Question

After hours of frustrating searches I feel I need to submit my question here. I apologize in advance if this question is somehow answered before but none of my searches has

Answer 1

Jeremy's answer is really good, though now Angular has changed, and will no longer work, unless you add this line of code:

$scope = $scope.$$childHead;

So, the changed function should look like this

function change() {
    var appElement = document.querySelector('[ng-app=myApp]');
    var $scope = angular.element(appElement).scope();
    $scope = $scope.$$childHead; // add this and it will work
    $scope.$apply(function() {
        $scope.data.age = 20;
    });
}