Calculate the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16. Which of the following choices is quartile 3?
• 8
• 6.5
• 2.5
• 9
To calculate the 5-number summary, we need to find the minimum, Q1 (1st quartile), median (Q2), Q3 (3rd quartile), and maximum.
1. The minimum value is 5.
2. Q1 (1st quartile) is the median of the lower half of the dataset (including the median if the dataset has an odd number of values). The lower half of the dataset is: 5, 6, 6, 7, 7. The median of this lower half is 6.
3. The median (Q2) of the entire dataset is the middle value, which is 8.
4. Q3 (3rd quartile) is the median of the upper half of the dataset (including the median if the dataset has an odd number of values). The upper half of the dataset is: 8, 9, 9, 14, 16. The median of this upper half is 9.
5. The maximum value is 16.
Therefore, the 5-number summary for this dataset is: 5, 6, 8, 9, 16.
Quartile 3 is the same as the 3rd quartile, which is 9. Therefore, the correct choice is:
• 9