To determine how the five-number summary changes with the addition of the score of 4 to the dataset \(3, 6, 2, 8, 6, 6, 9, 10, 3\), we first need to calculate the five-number summary of the original dataset, which consists of:
- Minimum
- First quartile (Q1)
- Median
- Third quartile (Q3)
- Maximum
Step 1: Order the original dataset The dataset ordered from lowest to highest is: \[ 2, 3, 3, 6, 6, 6, 8, 9, 10 \]
Step 2: Calculate the five-number summary of the original dataset
- Minimum: \(2\)
- Maximum: \(10\)
- Median (middle value for 9 data points): \(6\)
- Q1 (1st quartile, median of the first half): \(3\)
- Q3 (3rd quartile, median of the second half): \(8\)
Step 3: Add the score of 4 to the dataset The new dataset is: \[ 2, 3, 3, 4, 6, 6, 6, 8, 9, 10 \]
Step 4: Order the new dataset The new ordered dataset is: \[ 2, 3, 3, 4, 6, 6, 6, 8, 9, 10 \]
Step 5: Calculate the five-number summary of the new dataset
- Minimum: \(2\) (no change)
- Maximum: \(10\) (no change)
- Median: (average of the 5th and 6th values in a dataset with 10 points): \((6 + 6) / 2 = 6\) (no change)
- Q1 (median of the first half): the first half is \(2, 3, 3, 4, 6\) → Q1 is \(3\) (no change)
- Q3 (median of the second half): the second half is \(6, 6, 8, 9, 10\) → Q3 is \(8\) (no change)
Conclusion Adding the score of 4 does not change any part of the five-number summary. Therefore, none of the components (minimum, Q1, median, Q3, maximum) change with the addition of the score of 4.
Final Answer: None of the options provided (Q1, Q3, minimum, median) will change.