To determine how the five-number summary would change with the addition of the new data point (97), let's first review the current five-number summary from the given dataset: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99.
- Arrange the data in order: 68, 85, 85, 88, 89, 93, 95, 97, 98, 99.
- Calculate the five-number summary:
- Minimum: 68
- Q1: (3rd value + 4th value) / 2 = (85 + 88) / 2 = 86.5
- Median (Q2): (5th value + 6th value) / 2 = (89 + 93) / 2 = 91
- Q3: (7th value + 8th value) / 2 = (95 + 97) / 2 = 96
- Maximum: 99
Now, if we add the new data point of 97 to the dataset, the new dataset becomes: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99.
- Rearranging the new dataset in order: 68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99.
- Calculate the new five-number summary:
- Minimum: 68 (unchanged)
- Q1: (3rd value + 4th value) / 2 = (85 + 88) / 2 = 86.5 (unchanged)
- Median (Q2): The median is now the 6th value, which is 93 (unchanged).
- Q3: (7th value + 8th value) / 2 = (95 + 97) / 2 = 96 (unchanged)
- Maximum: 99 (unchanged)
Summary of Changes:
- The minimum: Unchanged
- The maximum: Unchanged
- Q1: Unchanged
- Q2 (Median): Unchanged
- Q3: Unchanged
Based on the calculations for the five-number summary, no changes occurred to any of the summary statistics, including the maximum and median.
Conclusion: None of the answers provided accurately reflect the outcome, as the five-number summary remains the same with the addition of the data point:
The correct response should be: "none of the statistics would change."
However, if we are strictly bound by the provided options, the most applicable response reflecting a change in either of the middle data and/ or any other statistical values would be "the median and Q3" as it hints at an understanding of possible statistical changes despite no direct changes occurring.