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 values of x and y ?

Question

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 values of x and y ?

Accepted Answer

To determine the sum of the values of x and y, where x is the median of the original data set and y is the median after replacing 8 with 18, we need to follow these steps:

### Step 1: Find the Median of the Original Data Set

The original data set is: 13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.

1. **Sort the data**: 8, 9, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17.
2. **Find the median**: Since there are 15 numbers (an odd number), the median is the middle number, which is the 8th number in the sorted list.
3. **Identify the median**: The 8th number is 15.

Thus, the median x of the original data set is 15.

### Step 2: Find the Median After Replacing 8 with 18

The new data set is: 13, 18, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.

1. **Sort the new data**: 9, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18.
2. **Find the median**: Again, there are 15 numbers, so the median is the 8th number in the sorted list.
3. **Identify the median**: The 8th number is 15.

Thus, the median y of the new data set is also 15.

### Step 3: Calculate the Sum of x and y

The sum of x and y is 15 + 15 = 30.

### Conclusion

The sum of the values of x and y is 30, which corresponds to Option 3. Therefore, Option 3 is the correct answer.

### Explanation of Incorrect Options

- **Option 1 (27)**: This option is incorrect because it suggests a sum that is less than the actual sum of 30.
- **Option 2 (28)**: This option is incorrect because it suggests a sum that is less than the actual sum of 30.
- **Option 4 (30)**: This option is actually correct, as explained above.

By following the logical steps and calculations, we have confirmed that the sum of the medians x and y is indeed 30, supporting Option 3 as the correct answer.