How to apply aggregation on the first field of first object of a array of objects in mongodb

Question

I have data in the format given below.

{
"_id" : 19,
"name" : "Gisela Levin",
"scores" : [
        {
                "score" : 44.51211101958831,
                "type" : "exam"
        },
        {
                "score" : 0.6578497966368002,
                "type" : "quiz"
        },
        {
                "score" : 93.36341655949683,
                "type" : "homework"
        }
],
"studentType" : "poor"}

Now i want to find the average of exam score for each studentType and i have written a query

db.student.aggregate( {$project : {_id : 0, studentType : 1, "scores.0.score" : 1}}, {$group : {_id : "$studentType", AverageMarks : {$avg : "$scores.0.score"}}} )

But i am getting this answer

{ "_id" : "good", "AverageMarks" : null }

{ "_id" : "avg", "AverageMarks" : null } { "_id" : "poor", "AverageMarks" : null }