Question

The dataset 3, 6, 2, 8, 6, 6, 9, 10, 3 represents the scores on the most recent quiz. Describe the change in the distribution of data if an additional number is added. If you add the score of 4, what part of the five-number summary will change?(1 point)
Responses

Q1
Q1

Q3
Q3

minimum
minimum

median

Answer 1

To analyze how adding the score of 4 to the dataset \(3, 6, 2, 8, 6, 6, 9, 10, 3\) affects the five-number summary, we first need to determine the five-number summary for the original dataset:

1. **Minimum**: The smallest value, which is \(2\).
2. **Q1 (First Quartile)**: The median of the lower half of the data. When the data is ordered: \(2, 3, 3, 6, 6, 6, 8, 9, 10\), Q1 is the median of \(2, 3, 3, 6\), which is \(3\).
3. **Median**: The middle value of the ordered dataset. For our ordered data, the median is \(6\) (the 5th value).
4. **Q3 (Third Quartile)**: The median of the upper half of the data, which is the median of \(6, 6, 8, 9, 10\), giving us \(8\).
5. **Maximum**: The largest value, which is \(10\).

Now, adding the score of 4 creates the new dataset: \(2, 3, 3, 4, 6, 6, 6, 8, 9, 10\).

Let’s determine the new five-number summary:

1. **New Minimum**: \(2\) remains the smallest.
2. **New Q1**: Now considering the lower half as \(2, 3, 3, 4, 6\), Q1 becomes the median of this set, which is \(3\) (the middle value).
3. **New Median**: In the new ordered dataset, the median (5th position) is still \(6\).
4. **New Q3**: For the upper half \(6, 6, 8, 9, 10\), Q3 remains \(8\) (the median of this segment).
5. **New Maximum**: \(10\) remains the largest value.

Upon adding the score of 4, the following parts of the five-number summary do not change: Minimum, Q1, Median, Q3, and Maximum all stay the same.

Therefore, since no parts of the five-number summary change after adding 4, your answer to the question is:

**None of the options provided (Q1, Q3, minimum, median) will change; thus, indicating that all values remain the same or none are applicable.**