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. (6 points) Minimum value: Maximum value: Median: Quartile 1: Quartile 3: IQR:

Answer 1

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

1. **Minimum value:** The smallest number in the dataset.
2. **Maximum value:** The largest number in the dataset.
3. **Median:** The middle value of the dataset.
4. **Quartile 1 (Q1):** The median of the first half of the dataset.
5. **Quartile 3 (Q3):** The median of the second half of the dataset.
6. **Interquartile Range (IQR):** The difference between Q3 and Q1.

**Step 1: Identify the minimum and maximum values**
- **Minimum value:** 5
- **Maximum value:** 16

**Step 2: Find the median**
Since there are 12 numbers (even count), the median will be the average of the 6th and 7th numbers in the sorted dataset.
- The 6th number is 8 and the 7th number is also 8.
- Median = \((8 + 8) / 2 = 8\)

**Step 3: Find Q1 and Q3**
To find Q1, we look at the first half of the data (the first 6 numbers): \(5, 6, 6, 7, 7, 8\)
- For Q1, we take the average of the 3rd (6) and 4th (7) numbers.
- Q1 = \((6 + 7) / 2 = 6.5\)

To find Q3, we look at the second half of the data (the last 6 numbers): \(8, 8, 9, 9, 14, 16\)
- For Q3, we take the average of the 3rd (9) and 4th (9) numbers.
- Q3 = \((9 + 9) / 2 = 9\)

**Step 4: Calculate the IQR**
- IQR = Q3 - Q1 = \(9 - 6.5 = 2.5\)

**Summary of 5-number summary:**
- Minimum value: **5**
- Maximum value: **16**
- Median: **8**
- Quartile 1 (Q1): **6.5**
- Quartile 3 (Q3): **9**
- IQR: **2.5**

**Final Values:**
- Minimum value: **5**
- Maximum value: **16**
- Median: **8**
- Quartile 1: **6.5**
- Quartile 3: **9**
- IQR: **2.5**