The median of a set of 11 distinct observations is 17.5. If each of the largest 5 observations of the set is increased by 3, then the median of the new set:

Options

A. is three times of the original number
B. is decreased by 3
C. is increased by 3
D. remains the same as that of the original set

Answer

To solve the problem step by step, we need to analyze the information given and how the median is affected by the changes made to the observations.

### Step-by-Step Solution:

1. **Understanding the Median**:
The median of a set of observations is the middle value when the observations are arranged in ascending order. For a set of 11 distinct observations, the median is the 6th observation when they are sorted.

2. **Identifying the Current Median**:
We are given that the median of the original set of 11 observations is 17.5. This means that the 6th observation in the sorted list of these observations is 17.5.

3. **Modifying the Observations**:
The problem states that each of the largest 5 observations is increased by 3. This means that the top 5 values in the sorted list will be increased, but we need to determine how this affects the median.

4. **Analyzing the Impact on the Median**:
Since the median is the 6th observation, we need to consider the position of the 6th observation after the largest 5 observations are increased by 3.
- The largest 5 observations are those that are greater than or equal to the 6th observation (17.5).
- Increasing these 5 largest observations by 3 will not affect the 6th observation (which is 17.5) because the 6th observation remains unchanged.

5. **Conclusion**:
Since the 6th observation (the median) remains the same and is unaffected by the changes made to the largest 5 observations, the median of the new set will still be 17.5.

### Final Answer:
The median of the new set is **17.5**.