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
if your answer is not one of the choices, you're wrong.

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
2. First quartile (Q1)
3. Median (Q2)
4. Third quartile (Q3)
5. Maximum

### Step 1: Sort the Data
The dataset is already sorted:
\[ 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16 \]

### Step 2: Calculate Minimum and Maximum
- Minimum = 5
- Maximum = 16

### Step 3: Calculate the Median (Q2)
The median (Q2) is the middle value. Since there are 12 values (even count), the median is the average of the 6th and 7th values.

- 6th value: 8
- 7th value: 8

\[
Q2 = \frac{8 + 8}{2} = 8
\]

### Step 4: Calculate Q1
Q1 is the median of the first half of the data (the first 6 values):
\[ 5, 6, 6, 7, 7, 8 \]

The median of this subset (6 values) is the average of the 3rd and 4th values.

- 3rd value: 6
- 4th value: 7

\[
Q1 = \frac{6 + 7}{2} = 6.5
\]

### Step 5: Calculate Q3
Q3 is the median of the second half of the data (the last 6 values):
\[ 8, 8, 9, 9, 14, 16 \]

The median of this subset (6 values) is the average of the 3rd and 4th values.

- 3rd value: 9
- 4th value: 9

\[
Q3 = \frac{9 + 9}{2} = 9
\]

### 5-Number Summary
Now we can compile the 5-number summary:
- Minimum: 5
- Q1: 6.5
- Median (Q2): 8
- Q3: 9
- Maximum: 16

### Conclusion
The third quartile (Q3) is **9**.

Thus, the answer to the question is:
**9**