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 minimum
the minimum

the maximum and the median
the maximum and the median

the median and Q3

Answer 1

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**