Let `x` be the median of the data
13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14. If 8 is replaced by 18, then the median of the data is `y`. What is the sum of the value of `x` and `y`?

Options

A. 28
B. 29
C. 30
D. 27

Answer

To find the sum of the medians \( x \) and \( y \) from the given data, we will follow these steps:

### Step 1: Arrange the original data in ascending order
The original data is:
\[ 13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14 \]

Arranging this data in ascending order gives:
\[ 8, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17 \]

### Step 2: Find the median \( x \) of the original data
The median is the middle value in a sorted list. Since there are 15 values (an odd number), the median is the value at position \( \frac{15 + 1}{2} = 8 \).

The 8th value in the sorted list is:
\[ 14 \]

Thus, \( x = 14 \).

### Step 3: Replace 8 with 18 in the original data
Now, we replace 8 with 18 in the original data:
\[ 18, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17 \]

### Step 4: Arrange the new data in ascending order
The new data in ascending order is:
\[ 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18 \]

### Step 5: Find the median \( y \) of the new data
Again, since there are 15 values, the median is the value at position \( \frac{15 + 1}{2} = 8 \).

The 8th value in the new sorted list is:
\[ 15 \]

Thus, \( y = 15 \).

### Step 6: Calculate the sum of \( x \) and \( y \)
Now, we find the sum:
\[ x + y = 14 + 15 = 29 \]

### Final Answer
The sum of the values of \( x \) and \( y \) is:
\[ \boxed{29} \]