To calculate the 5-number summary of the dataset \(15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29\), we first need to determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
- Minimum: The smallest value in the dataset is 15.
- Maximum: The largest value in the dataset is 29.
- Median (Q2): To find the median, we look for the middle value. Since there are 11 numbers (an odd count), the median is the 6th number in the ordered list. Thus, the median is 18.
- First Quartile (Q1): Q1 is the median of the first half of the dataset (the first 6 values): \(15, 16, 16, 17, 17, 18\). The median of these values (3rd and 4th: 16 and 17) is \(\frac{16 + 17}{2} = 16.5\).
- Third Quartile (Q3): Q3 is the median of the second half of the dataset (the last 6 values): \(18, 18, 19, 19, 29\). The median of these values (3rd and 4th: 19 and 19) is \(19\).
Putting it all together, the 5-number summary is:
- Minimum: 15
- Q1: 16.5
- Median (Q2): 18
- Q3: 19
- Maximum: 29
So, the 5-number summary is \(15, 16.5, 18, 19, 29\).
Now, regarding the box plot and why the dataset is skewed, the correct response would be:
The right whisker is much longer than the left whisker.
This indicates that the data has a longer range on the right side of the median, which is characteristic of a right-skewed distribution.