Ten people sit in a dentist’s waiting room. The mean number of fillings they have in their mouths is 4. Yet none of the 10 people actually have 4 fillings. Explain how this situation is possible.

These are all true statements. Explain why each one must be true.

At least one person has more than 4 fillings and at least one has fewer than 4 fillings.

No person has more than 40 fillings.

From 0–9 people could have 0 fillings.

At least 2 people must have fewer than the mean number of 4 fillings.

It is not possible that all 10 people have an equal number of fillings.