Dr. Greene's Answer
Speaking generally, the total amount of sleep a child gets is more important than how they schedule that sleep. The typical 2-year-old averages about 12-13 hours of sleep over 24 hours, but an hour or so more or less than that can be normal.
The average 2-year-old gets about 90 minutes of the total during the day as one or more naps — but again more or less than that can be fine.
Some individual children do fine with no nap at all at that age. Others seem to really benefit from a nap. When it comes to this, parents’ intuition is usually accurate about what their children need.