Question

Given the dataset 15, 10, 12, 11, 5, 8, 25, 30, 9, and 6, what parts of the five-number summary would change if a new data point of 15 was added?(1 point)
Responses

median
median

Q1, Q3
Q1, Q3

median, Q3
median, Q3

median, Q1, Q3, maximum, and minimum

Answer 1

To determine which parts of the five-number summary would change if a new data point of 15 was added to the dataset (15, 10, 12, 11, 5, 8, 25, 30, 9, 6), we first need to calculate the five-number summary for the original dataset:

1. **Minimum**: The smallest number in the dataset.
2. **Q1** (first quartile): The median of the first half of the dataset.
3. **Median**: The middle number when the data is ordered.
4. **Q3** (third quartile): The median of the second half of the dataset.
5. **Maximum**: The largest number in the dataset.

**Original Dataset**: 5, 6, 8, 9, 10, 11, 12, 15, 25, 30 (after sorting)

1. **Minimum**: 5
2. **Maximum**: 30
3. **Median**: The middle value (10th value, average of the 5th and 6th values) = (11 + 12) / 2 = 11.5
4. **Q1**: The median of the first half (5, 6, 8, 9, 10) = 8
5. **Q3**: The median of the second half (11, 12, 15, 25, 30) = 15

Now, we add a new data point of 15:

**New Dataset**: 5, 6, 8, 9, 10, 11, 12, 15, 15, 25, 30 (after sorting)

Now let’s recalculate the five-number summary:

1. **Minimum**: 5
2. **Maximum**: 30
3. **Median**: Now, there are 11 data points, so the median will be the 6th value = 11
4. **Q1**: Median of the first half (5, 6, 8, 9, 10) = 8
5. **Q3**: Median of the second half (11, 12, 15, 15, 25, 30) = 15

Comparing these summaries, we note that:

- The minimum remains **5** (no change)
- The maximum remains **30** (no change)
- **Median** has changed from **11.5** to **11**.
- **Q1** remains **8** (no change)
- **Q3** remains **15** (no change)

So, the parts of the five-number summary that would change are:

**Median and Q3.**

However, Q3 did not change—it remains the same at 15.

Thus, the correct answer is:

**Median.**