When picking fields for calculations, the selections do not show in the box once I hit ok

It worked for me:

You can try to use custom calculation instead, but first rename field Score.1 to Score_1 then use this as custom calculation script:

var count = 0;
var avg = 0;

for(var i=1; i<=10; i++){
 var f = this.getField("Score_"+i).valueAsString;
 if(f != "Select"){
  count++;
  avg += Number(f);}}
if( count == 0)
 event.value = "";
else
 event.value = avg/count;

Also you may want to check 'Commit selected value immediately' in all of score fields so you don't need to lose focus on the field (click outside field) for score to calculate, it's under 'Options' tab.

@chrissy_8224 I think it may be the text fields aren't named in a way that Acrobat can recognize for calculations. To fix this, go back and rename the text fields. Simply click on each field, find its properties, and give it a simple, unique name without any spaces or special characters, like "Score_1," "Score_2," and so on. This will allow Acrobat to "see" and use them in your calculations properly. Once you've renamed them, the selected fields should appear correctly after you hit "OK."