Explanation:

- The mean (average) of these numbers is 15.

- To find the mean, add all numbers together and divide by the number of numbers.

- The numbers are: 11, 10, 12, 13, 15, x, and 17.

- Total numbers = 7.

Total sum of numbers = 11 + 10 + 12 + 13 + 15 + x + 17.

- Total sum should equal 15 * 7 (since the mean is 15), so:

78 + x = 105.

- Solving for x:

x = 105 - 78 = 27.

- The value of x is thus 27.

- Correct Answer: Option 4 - 27