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

Answer 1

To calculate the 5-number summary of the dataset, we need to find:

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

**Given dataset:**
5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16

**Step 1: Minimum**
The minimum value is the smallest number in the dataset.
- Minimum = 5

**Step 2: Maximum**
The maximum value is the largest number in the dataset.
- Maximum = 16

**Step 3: Median (Q2)**
To find the median, we locate the middle value of the ordered dataset. Since there are 12 data points (even), the median will be the average of the 6th and 7th values.

Ordered dataset:
5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16

The 6th value = 8
The 7th value = 8

Median (Q2) = (8 + 8) / 2 = 8

**Step 4: First Quartile (Q1)**
Q1 is the median of the first half of the dataset (the first 6 values):
5, 6, 6, 7, 7, 8

For the 6 values, the median is the average of the 3rd and 4th values:
Q1 = (6 + 7) / 2 = 6.5

**Step 5: Third Quartile (Q3)**
Q3 is the median of the second half of the dataset (the last 6 values):
8, 8, 9, 9, 14, 16

For the 6 values, the median is also the average of the 3rd and 4th values:
Q3 = (9 + 9) / 2 = 9

**Five-number summary:**
- Minimum: 5
- Q1: 6.5
- Median (Q2): 8
- Q3: 9
- Maximum: 16

Thus, the 5-number summary is:
**5, 6.5, 8, 9, 16**