This encounter sparked my interest in maths around 12 years ago whilst in primary school and I just remembered it recently and I have no idea how it was done.
Our teacher showed the classroom (around 30 students) a jar full of plastic bears and stated that the number within the jar was between 700-750 and we should all estimate individually how many bears are within the jar. Once we had made our estimates, he asked us to calculate the collective mean average. After we had written our worked-out means on a sticky note he revealed the number in the jar and it had matched the mean average I had written down.
Here is the nuance: Given that out of a class of ~30 probably ~9-year-olds, the task was done by hand (leading to errors), and I was the only one with the "correct" solution was this by chance in that we had all done it wrong or was I the only person who had the correct mean and thus, had worked out the correct number of bears within the jar just from our group collective estimates alone?