To determine what parts of the five-number summary would change if a new data point of 97 was added to the dataset, we first need to calculate the five-number summary before and after the addition of the new data point.
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Initial Dataset: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99
- Minimum: 68
- Q1: The first quartile, or the median of the first half (68, 85, 85, 88, 89), is 85.
- Median: The median of the dataset (10 numbers) is the average of the 5th and 6th numbers, which are 89 and 95: \[(89 + 95) / 2 = 92\].
- Q3: The third quartile, or the median of the second half (89, 93, 95, 97, 98, 99), is 96.
- Maximum: 99
So, the initial five-number summary is:
- Minimum: 68
- Q1: 85
- Median: 92
- Q3: 96
- Maximum: 99
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Updated Dataset: 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99 (adding the new data point 97)
Now we sort this updated dataset:
- 68, 85, 85, 88, 89, 97, 97, 93, 95, 98, 99
Now we find the five-number summary again.
- Minimum: 68
- Q1: The first quartile (68, 85, 85, 88, 89) is still 85.
- Median: Now there are 11 data points, so the median is the 6th number, which is 97.
- Q3: The third quartile (97, 93, 95, 98, 99) is the median of this subset: 97.
- Maximum: 99
Now the updated five-number summary is:
- Minimum: 68
- Q1: 85
- Median: 97
- Q3: 97
- Maximum: 99
Conclusion:
The changes are as follows:
- The median changed from 92 to 97.
- The Q3 changed from 96 to 97.
- The minimum and maximum remain the same, and Q1 remains the same.
The correct response is: the median and Q3.
1 answer