If the median of 25 observations is 45 and if the observations greater than the median are increased by 4, then the median of the new data is

Options

A. 49
B. 41
C. 45
D. none of these

Explanation

To solve the problem step by step, we will analyze the given information and apply the properties of the median.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have 25 observations, and the median of these observations is 45.

2. **Identifying the Median**:
- Since there are 25 observations (an odd number), the median is the value at the 13th position when the observations are arranged in ascending order. This means that the 13th observation is 45.

3. **Modifying the Observations**:
- The problem states that we increase all observations greater than the median (i.e., greater than 45) by 4.

4. **Analyzing the Impact on the Median**:
- The observations that are equal to or less than 45 will remain unchanged.
- The observations that are greater than 45 will increase by 4, but their positions in the ordered list will remain the same.

5. **Finding the New Median**:
- Since the median is the middle value, we need to check the new values in the 13th position and the surrounding positions.
- The 13th observation remains 45, and the observations in positions 14 to 25 will increase by 4.
- Thus, the new values in positions 14 to 25 will be greater than 45 (specifically, they will be greater than or equal to 49).

6. **Conclusion**:
- Since the 13th observation is still 45 and the 14th observation (which is now greater than 45) will be the next value in the ordered list, the new median will still be the value at the 13th position, which is 45.

### Final Answer:
The median of the new data remains **45**.