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 given dataset, we need to identify the following five values: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

The dataset is:
5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16

1. **Minimum**: The smallest value in the dataset.
- **Minimum** = 5

2. **Maximum**: The largest value in the dataset.
- **Maximum** = 16

3. **Median (Q2)**: The middle value when the data is arranged in order. Since there are 12 numbers (an even number), the median will be the average of the two middle numbers.
- The two middle numbers are the 6th and 7th values in the ordered list: 8 and 8.
- **Median (Q2)** = (8 + 8) / 2 = 8

4. **First Quartile (Q1)**: The median of the first half of the data. The first half consists of the first 6 values: 5, 6, 6, 7, 7, 8.
- The median of this subset is the average of the 3rd and 4th values (6 and 7).
- **Q1** = (6 + 7) / 2 = 6.5

5. **Third Quartile (Q3)**: The median of the second half of the data. The second half consists of the last 6 values: 8, 9, 9, 14, 16.
- The median of this subset is the average of the 3rd and 4th values (9 and 14).
- **Q3** = (9 + 14) / 2 = 11.5

Putting it all together, the 5-number summary is:
- Minimum = 5
- Q1 = 6.5
- Median (Q2) = 8
- Q3 = 11.5
- Maximum = 16

**5-number summary**: (5, 6.5, 8, 11.5, 16)