Adobe Acrobat Pro - Calculate Average of only checked boxes

This functionality is just complicated enough that a custom script will be needed.

But first, the checkbox field names will need to be changed, so they are suitable for scripting. 

Make them something like "Question1.Check1", "Question1.Check2", "Question1.Check3", etc.

Here's a custom calculation script for the result field.

 // First, get an array of all the checkbox fields for this question
var aChkFields = this.getField("Question1").getArray();

// Loop over array and sum only checkboxes that are checked. 
var nSum = 0, nCnt = 0;
for(var i=0;i<aChkFields.length;i++)
{
    if((aChkFields[i].value != "Off") && !isNaN(aChkFields[i].value)){
       nCnt++;
       nSum += Number(aChkFields[i].value);
    }
}
if(nCnt > 0)
  event.value = nSum/nCnt;
else
  event.value = "";