To determine how the five-number summary is affected by adding another data point of 97 to the dataset, we first calculate the original five-number summary:
- Minimum: 68
- Q1 (First Quartile): The median of the first half (68, 85, 85, 88, 89) is 85.
- Median: The median of the entire dataset (68, 85, 85, 88, 89, 93, 95, 97, 98, 99) is the average of 89 and 93, which is 91.
- Q3 (Third Quartile): The median of the second half (89, 93, 95, 97, 98, 99) is 95.
- Maximum: 99
Now, let's add the new data point of 97 to the dataset:
New dataset: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99
Next, we recalculate the five-number summary:
- Minimum: Still 68
- Q1: The first half is still (68, 85, 85, 88, 89), so Q1 remains 85.
- Median: The new median is the average of the 5th and 6th values from the sorted list: 89 and 93. This gives a new median of 91.
- Q3: The second half is (89, 93, 95, 97, 97, 98, 99). The median of this half, which is the average of 95 and 97, is now 95.
- Maximum: Still 99
After adding the new data point:
- Minimum remains the same (68).
- Q1 remains the same (85).
- Median (91) does not change.
- Q3 (95) remains the same.
- Maximum remains the same (99).
Now we compare it to the original summary. The Median and Q3 values would not change.
Thus, none of the values actually change.
The correct response is:
- the minimum
This would not change also, therefore none of the components are affected, and the question seems to mislead as all remain the same.
However, to correctly reflect what's affected by the change in dataset, referencing the original dataset:
If choosing from the statements listed, one should reconsider original median effect, as the median stays the same, impacting none fully after reaffirming their specifics.
Based on the summary statement change, the closest response is none, signifying all remain valid against additive checks per standard distribution metrics across 5-number summarization, maintaining high accuracy against claims to originals.
In official choice referencing, if any implied aspect must not change, contextually:
Best option remains the minimum and median, significantly illustrating joint values under stable ranges through extra additions, as median backed under 5-number (anchored values) formatting indicates ranges maintaining.