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 minimum
the minimum

the median
the median

the maximum and the median
the maximum and the median

Answer 1

To determine how adding a new data point of 97 to the dataset affects the five-number summary, let's first calculate the five-number summary of the original dataset:

Original dataset: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99

1. **Minimum**: 68
2. **Q1 (First quartile)**: The median of the first half (68, 85, 85, 88, 89) = 85
3. **Median**: (97 + 89) / 2 = 93.0 (since the dataset has an even number of elements)
4. **Q3 (Third quartile)**: The median of the second half (93, 95, 98, 99) = 96.5
5. **Maximum**: 99

Now, we add the new data point (97) to the dataset.

New dataset: 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99

1. **Minimum**: 68 (unchanged)
2. **Q1**: This value remains the same because the lower half of the dataset (up to the new median) is still structured similarly.
3. **Median**: There are now 11 data points. The median is the middle value, located at the 6th position, which is 97.
4. **Q3**: The third quartile will change because the upper half of the dataset now includes the additional 97. This affects the calculations for the new Q3.
5. **Maximum**: 99 (unchanged)

Thus, with the addition of the new point of 97, the median will change to 97, and Q3 will also change.

So the answer is:
**the median and Q3**.