Unless you're tracking your attempts, that average is a feeling, not a statistic, and humans are bad at math.
The drop rate for shards is about a third. That means the chance of getting five shards from five attempts is between half and a quarter of a percent. The chance of getting zero shards from five attempts is about thirteen percent. One of these happening repeatedly is more common than the other.
The average shard drop per day is about one and two thirds.
Farming from zero to 7* with five node attempts per day every day will take, on average, 198 days.