Question

Calculate the values for the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.(2 points)
The minimum value=
. The maximum value=
. The median=
. Quartile 1=
. Quartile 3=
.

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 determine the following values:

1. **Minimum**: The smallest value in the dataset.
2. **Maximum**: The largest value in the dataset.
3. **Median**: The middle value of the dataset.
4. **Quartile 1 (Q1)**: The median of the lower half of the dataset.
5. **Quartile 3 (Q3)**: The median of the upper half of the dataset.

### Step-by-step Calculation

1. **Minimum**:
- The minimum value is \(5\).

2. **Maximum**:
- The maximum value is \(16\).

3. **Median**:
- The median is the average of the 6th and 7th values in the ordered dataset.
- \(8\) (6th value), \(8\) (7th value).
- Median = \(\frac{8 + 8}{2} = 8\).

4. **Quartile 1 (Q1)**:
- Q1 is the median of the lower half of the dataset: \(5, 6, 6, 7, 7, 8\) (first 6 values).
- The median of this subset is the average of the 3rd and 4th values: \(6\) (3rd), \(7\) (4th).
- Q1 = \(\frac{6 + 7}{2} = 6.5\).

5. **Quartile 3 (Q3)**:
- Q3 is the median of the upper half of the dataset: \(8, 9, 9, 14, 16\) (last 6 values).
- The median of this subset is the average of the 3rd and 4th values: \(9\) (3rd), \(14\) (4th).
- Q3 = \(\frac{9 + 14}{2} = 11.5\).

### Summary of Results
- Minimum value = **5**
- Maximum value = **16**
- Median = **8**
- Quartile 1 = **6.5**
- Quartile 3 = **11.5**

Thus, the 5-number summary is:
- **Minimum**: 5
- **Maximum**: 16
- **Median**: 8
- **Q1**: 6.5
- **Q3**: 11.5