Ten observations 5, 9, 14, 15, x+1, 2x-13, 28, 30, 32, 34 are written in…

For any set of n observations arranged in ascending order, the median is defined differently depending on whether n is odd or even. When n is even, there is no single middle observation, so the median is defined as the average of the two central terms — the (n/2)-th and the (n/2 + 1)-th observations in the sorted list.

1. Here n = 10, an even count, so the median is the average of the 5th and 6th terms in the ascending list.

2. From the given ascending sequence 5, 9, 14, 15, x+1, 2x-13, 28, 30, 32, 34, the 5th term is x+1 and the 6th term is 2x-13.

3. Since the median is given as 24, set up the equation: (x + 1 + 2x - 13) / 2 = 24.

4. Simplify the numerator: (3x - 12) / 2 = 24.

5. Multiply both sides by 2: 3x - 12 = 48.

6. Add 12 to both sides: 3x = 60.

7. Divide by 3: x = 20.

Substituting x = 20 back into the sequence gives the 5th term = 21 and the 6th term = 27. The full ordered sequence 5, 9, 14, 15, 21, 27, 28, 30, 32, 34 remains correctly in ascending order, and the average of the two middle terms is (21 + 27) / 2 = 24, which matches the given median — confirming the value is correct.