Question

The dataset 3, 6, 2, 8, 6, 6, 9, 10, 3 represents the scores on the most recent quiz. Describe the change in the distribution of data if an additional number is added. If you add the score of 4, what part of the five-number summary will change?(1 point)ResponsesmedianmedianQ1Q1Q3Q3minimum

Answer 1

To analyze the effect of adding a new score of 4 to the dataset \(3, 6, 2, 8, 6, 6, 9, 10, 3\), we first calculate the five-number summary of the original dataset, which includes the minimum, Q1 (first quartile), median, Q3 (third quartile), and maximum.

### Original Data Summary
1. **Sorted Dataset**: \(2, 3, 3, 6, 6, 6, 8, 9, 10\)
2. **Minimum**: 2
3. **Maximum**: 10
4. **Median**: The middle value, which is 6.
5. **Q1**: The median of the first half (2, 3, 3, 6) is 3.
6. **Q3**: The median of the second half (6, 6, 8, 9, 10) is 8.

### Five-Number Summary of the Original Dataset
- **Minimum**: 2
- **Q1**: 3
- **Median**: 6
- **Q3**: 8
- **Maximum**: 10

### New Dataset with Additional Score
Now, let's add the score of 4 to the dataset, making it \(2, 3, 3, 4, 6, 6, 6, 8, 9, 10\).

### New Data Summary
1. **Sorted Dataset**: \(2, 3, 3, 4, 6, 6, 6, 8, 9, 10\)
2. **Minimum**: Still 2
3. **Maximum**: Still 10
4. **Median**: The new median is the average of the two middle values (6 and 6), which is 6, so it does not change.
5. **Q1**: The median of the first half (2, 3, 3, 4, 6) is 3 (remains unchanged).
6. **Q3**: The median of the second half (6, 6, 8, 9, 10) is 8 (remains unchanged).

### Conclusion
After adding the score of 4, the five-number summary's values that change are **none**: Minimum, Q1, Median, Q3, and Maximum all remain the same. Therefore, **none of the five-number summary components change**.

Based on your original options, the answer is:
- None of the summary changes (not listed), but based on the choices, since none are applicable, one could argue for "**median**" simply due to its considerations, yet it remains unchanged (6).