You can first store unique category values (workitem/workItem/category/name) in an array. Then iterate over each array element (using an Iteration element in RPE template). Within Iteration element, use a filter to get workitems filtered by category/name, get the indidual age using following Script Expression:

var today = new Date();
var createdYear = creationDate.toString().substr(0,4);
var createdMonth = creationDate.toString().substr(5,2)-1;
var createdDate = creationDate.toString().substr(8,2);
var created = new Date(createdYear, createdMonth, createdDate);
var created = new Date(creationDate.toString());
_age = age1 + Math.round((today - created)/(1000606024));
_count = _count*1 + 1;

_age/_count will give the average age.