Explanation:

- The average of 25 numbers is given as 13. So, the total sum of these numbers is 25 x 13 = 325.

- The average of the first 13 numbers is 11.5, and their total sum is 13 x 11.5 = 149.5.

- The average of the last 13 numbers is 14.5, and their total sum is 13 x 14.5 = 188.5.

- The middle number (13th in the sequence) overlaps in both groups and is counted twice.

- To find the middle number, add the sums of the first and last sets (149.5 + 188.5 = 338), then subtract the total sum of 25 numbers (338 - 325 = 13).

- Hence, the middle number is 13.

- Option 3: 13 is the correct answer.