To find out how the distribution of the data is affected by adding the score of 4, we first need to compute the five-number summary for the original dataset: 3, 6, 2, 8, 6, 6, 9, 10, 3.
- Minimum: The smallest value is 2.
- Q1 (First Quartile): This is the median of the lower half (excluding the median if the number of values is odd). The lower half is 2, 3, 3, 6. The median of these numbers is \((3 + 3)/2 = 3\).
- Median (Q2): The median for the entire dataset (when sorted: 2, 3, 3, 6, 6, 6, 8, 9, 10) is 6.
- Q3 (Third Quartile): This is the median of the upper half (6, 6, 8, 9, 10). The median of these numbers is 8.
- Maximum: The largest value is 10.
Now, the five-number summary for the original dataset (before adding 4) is:
- Minimum: 2
- Q1: 3
- Median: 6
- Q3: 8
- Maximum: 10
Next, we add the score of 4 to the dataset. The new dataset becomes: 2, 3, 3, 4, 6, 6, 6, 8, 9, 10.
Now, let's recalculate the five-number summary:
- Minimum: 2 (remains unchanged)
- Q1: The lower half is now 2, 3, 3, 4, 6. The new median of this half is \((3 + 4)/2 = 3.5\); therefore, Q1 changes to 3.5.
- Median (Q2): The median for the new dataset (sorted: 2, 3, 3, 4, 6, 6, 6, 8, 9, 10) is \((6 + 6)/2 = 6\) (remains unchanged because we have an even number of entries).
- Q3: The upper half is now 6, 6, 8, 9, 10. The median of this subset is 8 (remains unchanged).
- Maximum: 10 (remains unchanged).
In conclusion, when the score of 4 is added to the dataset, the only part of the five-number summary that changes is Q1, which changes from 3 to 3.5.
So the correct response is: Q1
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