A possible dataset is: -2, 12, 12, 18, 19, 21, 25.
An odd size means that 18 is the central data value. The question implies that 7 is the minimum size.
The sum of the data must be 7×15=105.
If x is the lowest value then x+27 is the highest and the dataset looks like:
x, 12, 12, 18, ..., ..., x+27. If we represent the sum of the two missing data as S, then:
105=2x+S+69, so 2x+S=36. Also x+27>18, so x>-9, and x<12. There needs to be room to slot in two data values between 18 and x+27. If x=-8, for example, then x+27=19. There is insufficient room to insert two integers between 18 and 19. S=36-2x, so if x<0, there are more possible choices for the missing data. When x=-2, S=40 and this allows 19 and 21 to be candidates. If x=-3, x+27=24, S=42, so 20 and 22 could also be candidates:
-3, 12, 12, 18, 20, 22, 24. Also, -3, 12, 12, 18, 19, 23, 24.