Illustrative data: 60 of 100 eligible people participate in one period; 90 of 200 participate in another. What happens to the participation count and rate?

Answer & explanation

The count rises while the rate falls from 60% to 45%.

The denominator changes from 100 to 200. Dividing participants by the relevant population gives a lower proportion in the second period despite more participants. These are invented numbers, not findings from Putnam's book.