1. **Problem Statement:** Find the median of the observations arranged in ascending order: 11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41. Given that the median is 24, find the value of $x$. 2. **Formula and Rules:** The median of a data set arranged in ascending order is the middle value if the number of observations is odd, or the average of the two middle values if even. 3. **Step-by-step Solution:** - There are 10 observations, so the median is the average of the 5th and 6th terms. - The 5th term is $x+2$ and the 6th term is $x+4$. - Median $= \frac{(x+2) + (x+4)}{2} = \frac{2x + 6}{2} = x + 3$ - Given median is 24, so: $$x + 3 = 24$$ - Solve for $x$: $$x = 24 - 3 = 21$$ 4. **Final Answer:** The value of $x$ is **21**.