Question

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)
Responses

the median
the median

the median and Q3
the median and Q3

the minimum
the minimum

the maximum and the median

Answer 1

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

1. **Minimum:** The smallest value (68)
2. **Q1:** The first quartile, which is the median of the first half (68, 85, 85, 88, 89) = 85
3. **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
4. **Q3:** The third quartile is the median of the second half (89, 93, 95, 97, 98, 99) = 95
5. **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:

1. **Minimum:** Remains (68)
2. **Q1:** Calculated from (68, 85, 85, 88, 89, 97) = 85
3. **Median:** New median position is now the 6th and 7th numbers (89 and 97). The new median= (89+97)/2 = 93
4. **Q3:** New Q3 calculated from (93, 95, 97, 98, 99) = 97
5. **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**.