Given the dataset 68, 85, 88, 97, 85, 89, 98, 93, 95, and 99, what parts of the five-number summary would change if a new data point of 97 was added?(1 point)

Question

Responses

the minimum
the minimum

the median and Q3
the median and Q3

the median
the median

the maximum and the median

Answer 1

To determine which parts of the five-number summary would change with the addition of the new data point (97), let's first calculate the five-number summary of the original dataset:

Original dataset: 68, 85, 88, 97, 85, 89, 98, 93, 95, 99.

1. Minimum: The smallest value, which is 68.
2. First Quartile (Q1): The median of the first half of the data (68, 85, 85, 88, 89). Here, Q1 is the median of 85 and 85, which is 85.
3. Median: The middle value of the sorted dataset. The sorted dataset is already in order, and since there are 10 values, the median is the average of the 5th and 6th values, which is (89 + 97)/2 = 93.
4. Third Quartile (Q3): The median of the second half of the data (97, 98, 93, 95, 99). Q3 is the median of 93 and 95, which is 94.
5. Maximum: The largest value, which is 99.

With the new data point of 97 added, the dataset becomes: 68, 85, 85, 88, 89, 97, 97, 98, 93, 95, 99.

Now, let's recalculate the five-number summary:

1. Minimum: Still 68.
2. First Quartile (Q1): The first half is 68, 85, 85, 88, 89 (which remains unchanged), so Q1 is still 85.
3. Median: Now we have 11 values, so the median is the 6th value in the sorted dataset, which is 97.
4. Third Quartile (Q3): The second half is 97, 98, 93, 95, 99. The median of that half is still (95 + 97)/2 = 96.
5. Maximum: Still 99.

So, after adding the new data point, the changes are:

• The median has changed from 93 to 97.
• Q3 has changed from 94 to 96.

Given the provided options, the correct response is "the median and Q3."