Question

Calculate the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16. Which of the following choices is quartile 3?(1 point) Responses 9 9 8 8 6.5 6.5 2.5
pick the best option

Answer 1

To calculate the 5-number summary of the dataset \( 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \), we need to find the following:

1. **Minimum**: The smallest number in the dataset.
2. **First Quartile (Q1)**: The median of the first half of the dataset.
3. **Median (Q2)**: The median of the entire dataset.
4. **Third Quartile (Q3)**: The median of the second half of the dataset.
5. **Maximum**: The largest number in the dataset.

Let's calculate these steps:

1. **Minimum**: The smallest number is \( 5 \).

2. **Maximum**: The largest number is \( 16 \).

3. **Median (Q2)**:
- Since there are 12 numbers (even count), the median will be the average of the 6th and 7th numbers.
- The 6th and 7th numbers are both \( 8 \).
- Thus, \( Q2 = \frac{8 + 8}{2} = 8 \).

4. **First Quartile (Q1)**:
- The first half of the dataset is \( 5, 6, 6, 7, 7, 8 \).
- The median of this half (6 numbers) will be the average of the 3rd and 4th numbers.
- The 3rd and 4th numbers are \( 6 \) and \( 7 \).
- Thus, \( Q1 = \frac{6 + 7}{2} = 6.5 \).

5. **Third Quartile (Q3)**:
- The second half of the dataset is \( 8, 8, 9, 9, 14, 16 \).
- The median of this half (6 numbers) will be the average of the 3rd and 4th numbers.
- The 3rd and 4th numbers are \( 9 \) and \( 9 \).
- Thus, \( Q3 = \frac{9 + 9}{2} = 9 \).

Now, we have the 5-number summary:

- Minimum: \( 5 \)
- First Quartile (Q1): \( 6.5 \)
- Median (Q2): \( 8 \)
- Third Quartile (Q3): \( 9 \)
- Maximum: \( 16 \)

The value of quartile 3 (Q3) is \( 9 \).

Among the choices given, the best option for quartile 3 is:
**9**.