This reminds me of a quote from dr. House. In one of the episodes with the smart girl that also studied mathematics (I don't remember her name), Cuddy said something like "You will figure this out, the sum of your IQs is over X". To which House replied, "The same applies to a group of four stupid people".

Sometimes knowledge and experience aren't additive: if none of the students had a certain experience/knows a certain fact, the sum of the students will still not have that experience or not know the fact.