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

median
median

Q1
Q1

minimum
minimum

Q3 wich one?

Answer 1

To determine how the addition of the score of 4 will affect the five-number summary, we first need to find the current five-number summary of the dataset:

1. The minimum
2. The first quartile (Q1)
3. The median
4. The third quartile (Q3)
5. The maximum

The original dataset is: **3, 6, 2, 8, 6, 6, 9, 10, 3**

First, let's sort the dataset: **2, 3, 3, 6, 6, 6, 8, 9, 10**

Now we can calculate the five-number summary:

- Minimum: **2**
- Q1: The median of the first half (2, 3, 3) is **3**
- Median: The middle value of the sorted list (6)
- Q3: The median of the second half (6, 8, 9, 10) is **8**
- Maximum: **10**

Now, if we add the score of 4, the new dataset will be: **2, 3, 3, 4, 6, 6, 6, 8, 9, 10**.

Sorting this gives: **2, 3, 3, 4, 6, 6, 6, 8, 9, 10**

Now let's calculate the new five-number summary:

- Minimum: **2** (no change)
- Q1: The first quartile is now the median of the first half (2, 3, 3, 4) which is the average of 3 and 3, so Q1 remains **3**.
- Median: The middle value of the sorted list (6), still remains the same, since there are now 10 numbers (mean of the 5th and 6th value).
- Q3: The median of the second half (6, 6, 8, 9, 10) is now the average of 6 and 8 which becomes **7** (this changes).
- Maximum: **10** (no change)

So, the only part of the five-number summary that changes when we add the score of 4 is **Q3**.