To determine what parts of the five-number summary would change if a new data point of 97 were added to the dataset, 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: The smallest value (68)
- Q1: The first quartile, which is the median of the first half (68, 85, 85, 88, 89) = 85
- Median: The median (average of 10 numbers) is the average of the 5th and 6th values in sorted order (89 and 90) = (89+90)/2 = 88.5
- Q3: The third quartile is the median of the second half (89, 93, 95, 97, 98, 99) = 95
- Maximum: The largest value (99)
New Dataset with 97 added: 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99
Now we need to recalculate the five-number summary:
- Minimum: Remains (68)
- Q1: Calculated from (68, 85, 85, 88, 89, 97) = 85
- Median: New median position is now the 6th and 7th numbers (89 and 97). The new median= (89+97)/2 = 93
- Q3: New Q3 calculated from (93, 95, 97, 98, 99) = 97
- Maximum: Remains (99)
Summary of Changes
- The median changed from 89 to 93.
- The Q3 changed from 95 to 97.
- The minimum and maximum did not change.
Answer
Therefore, if a new data point of 97 is added, the parts of the five-number summary that would change are the median and Q3.
The correct response is: the median and Q3.