[{"_id":"xxx","name":"some_name","data":{"first_thing":[1,2,3,4],"second_thing":[5,3,2,4],}}]

db.collection.aggregate([{"$project":{"_id":"$name","data.first_thing.mean":{"$avg":"$data.first_thing"},"data.first_thing.std":{"$stdDevPop":"$data.first_thing"}}},{"$unwind":"$data.first_thing"},{$group:{_id:"$_id",data:{$addToSet:{first_thing:["$data.first_thing"]}}}}])