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
- Minimum: 68
- Q1 (First quartile): The median of the first half (68, 85, 85, 88, 89) = 85
- Median: (97 + 89) / 2 = 93.0 (since the dataset has an even number of elements)
- Q3 (Third quartile): The median of the second half (93, 95, 98, 99) = 96.5
- 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
- Minimum: 68 (unchanged)
- Q1: This value remains the same because the lower half of the dataset (up to the new median) is still structured similarly.
- Median: There are now 11 data points. The median is the middle value, located at the 6th position, which is 97.
- 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.
- 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.