The average number of students is calculated by dividing the sum of the number of students in all colleges by the number of colleges:
\[
\text{Average} = \frac{1000 + 1500 + 1200 + 1300 + 900}{5}
\]
\[
\text{Average} = \frac{5900}{5} = 1200
\]
Answer: Therefore, the average number of students is 1200. So, the correct answer is option (1).