Question

Given the dataset 68, 85, 88, 97, 85, 89, 98, 93, 95, and 99, what parts of the five-number summary would change if a new data point of 97 was added?(1 point)
Responses

the median and Q3
the median and Q3

the median
the median

the minimum
the minimum

the maximum and the median

Answer 1

To determine which parts of the five-number summary would change if a new data point of 97 was added to the dataset (68, 85, 88, 97, 85, 89, 98, 93, 95, and 99), let's first analyze the current five-number summary.

**1. Current Data and Five-Number Summary:**
- **Sorted dataset**: 68, 85, 85, 88, 89, 93, 95, 97, 98, 99
- **Minimum (Min)**: 68
- **First Quartile (Q1)**: The median of the first half (68, 85, 85, 88, 89) is 85.
- **Median**: The median of the entire dataset (93.5, the average of 93 and 95) is 93.5.
- **Third Quartile (Q3)**: The median of the second half (97, 98, 99) is 98.
- **Maximum (Max)**: 99

**2. Adding the New Data Point (97):**
The new dataset is 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99.

**3. Updated Five-Number Summary:**
- **Sorted dataset**: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99
- **Minimum (Min)**: 68 (remains the same)
- **First Quartile (Q1)**: Still the median of (68, 85, 85, 88, 89) = 85.
- **Median**: The total number of data points is now 11. The median is the 6th number in the sorted list, which is now 93 (remains the same).
- **Third Quartile (Q3)**: The upper half is now (97, 97, 98, 99). The median of this is (97 + 98) / 2 = 97.5. (Q3 changes)
- **Maximum (Max)**: 99 (remains the same)

**4. Summary:**
After adding 97 to the dataset, the median remains the same, but Q3 changes.

Therefore, the correct response is:

**the median and Q3**