There are two sets of data: the mean of the first set is $15$, and the mean of the second set is $20$.

One of the pieces of data from the first set is exchanged with one of the pieces of data from the second set.

As a result, the mean of the first set of data increases from $15$ to $16$, and the mean of the second set of data decreases from $20$ to $17$.

What is the mean of the set made by combining all the data?