Final answer:
The mode is the most frequently appearing number in a data set. In this case, forty-one and one third appears five times, making it the mode of the data set.
Step-by-step explanation:
The mode of a data set is the number that appears most frequently. In the provided data set, we can count the frequency of each number and determine which one occurs most often.
Here is the frequency of each number in the data set:
- Twelve and one third: 3 times
- Eighteen and two thirds: 2 times
- Twenty-one and two thirds: 3 times
- Forty-one and one third: 5 times
Since forty-one and one third appears 5 times, which is more than any other number, it is the mode of this data set.
Therefore, the correct answer is D. forty-one and one third.