solution: The median of a set of consecutive positive integers is equal to the mean of the set of integers.  Therefore, we can find the median by dividing the sum by the number of integers: $3^7/3^3=3^4=\boxed{81}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The sum of 27 consecutive positive integers is $3^7$. What is their median?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 81
extra_info.question: The sum of 27 consecutive positive integers is $3^7$. What is their median?
extra_info.split: test