To determine how the five-number summary is affected by adding a new data point of 97 to the dataset, we first need to find the five-number summary of the original dataset and then see how it changes.
The original dataset is: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99
Step 1: Original Five-Number Summary
- Minimum: 68
- Q1: 85 (25th percentile)
- Median: (89 + 88) / 2 = 88.5 (the average of the 5th and 6th values when arranged)
- Q3: 95 (75th percentile)
- Maximum: 99
Step 2: Add the new data point (97) The new dataset becomes: 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99
This new dataset rearranged in order is: 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99
Step 3: New Five-Number Summary
- Minimum: 68 (remains unchanged)
- Q1: 85 (remains unchanged)
- Median: Now, with an odd number of data points (11 values), the median is 97 (the 6th value).
- Q3: This also remains as it corresponds to the 75th percentile and is still 95 (remains unchanged).
- Maximum: 99 (remains unchanged)
Thus, the changes are:
- The median changes from 88.5 to 97.
Conclusion: The correct response is: the median
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