To determine how the five-number summary changes with the addition of a new data point (97) to the dataset, we first need to define the five-number summary, which consists of:
- Minimum
- Q1 (first quartile)
- Median (Q2)
- Q3 (third quartile)
- Maximum
The original dataset is: 68, 85, 85, 88, 89, 93, 95, 97, 98, 99.
Now, let's see what happens when we add another data point of 97:
- New Dataset: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99.
- New Maximum: The maximum remains 99.
- New Minimum: The minimum remains 68.
- New Median: The median of the new dataset (11 values) is the average of the 5th and 6th values, which are 89 and 93, so the median is (89 + 93) / 2 = 91. This is the same as the original median of 91, therefore it does not change.
- New Q1: The first quartile (Q1) is the median of the first half (first 5 values - 68, 85, 85, 88, 89), which is 85. This remains unchanged.
- New Q3: The third quartile (Q3) is the median of the second half (last 5 values - 93, 95, 97, 97, 98, 99), which is the average of 97 and 98, resulting in Q3 = (97 + 98)/2 = 97.5. Since the original Q3 was 96, this value has changed to 97.5.
Thus, the only part of the five-number summary that changes is:
- The median remains the same (91).
- The Q3 value has changed from 96 to 97.5.
To summarize, the change occurs in Q3, but since none of the responses only mentions Q3, the best answer based on the options provided would be:
"The median and Q3"
However, since the median does not actually change, the correct logical response would emphasize that only Q3 changes. If the quiz context allows for focusing solely on the changes specifically to Q3, that would be more precise, but given the responses, it might still reflect the confusion over the distinction.
In this case, the choice would likely lead to:
"The median and Q3" (with the understanding that the median remains strictly unchanged).