When the numbers in a data set are arranged from smallest to largest, if the number of data is odd, the median (middle value) is the middle number; if the number of data is even, the median is the arithmetic mean of the two middle numbers.
Consisting of distinct integers and arranged from smallest to largest
$$9, 10, a, 13, 16, b$$
the arithmetic mean and median of the data set are consecutive integers.
Accordingly, what is the sum $a + b$?
A) 30
B) 36
C) 42
D) 48
E) 54