How Elasticsearch calculate average if there are multiple shards

example.txt

# Create an index with 2 primary shards.
PUT avg-avg
{
  "settings": {
    "number_of_shards": 2,
    "number_of_replicas": 0
  }
}

# Add some documents.
POST avg-avg/_bulk
{"index": {"_id": "1"}}
{"v": 100}
{"index": {"_id": "2"}}
{"v": 100}
{"index": {"_id": "3"}}
{"v": 100}
{"index": {"_id": "a"}}
{"v": 100}
{"index": {"_id": "b"}}
{"v": 1}
{"index": {"_id": "c"}}
{"v": 100}

# With explain, we can find which shard a document resides.
# Doc 'b' resides in shard 1. The rest is in shard 0
GET avg-avg/_search
{
  "explain": true
}

# If ES calculates overall avg, it should be:
# (500 + 1) / 6 = 83.5
# But if shard level avg, then avg of avg, it would be:
# (100 + 1) / 2 = 50.5
GET avg-avg/_search
{
  "size": 0,
  "aggs": {
    "avg": {
      "avg": {
        "field": "v"
      }
    }
  }
}