To determine the mode of the distribution of years served by the 99 U.S. Supreme Court Justices, we need to find the number of years that appears most frequently in the dataset.
A mode is the value that appears most frequently in a data set.
1. Step-by-step breakdown:
- List out all the frequencies of each year.
- Identify the year with the highest frequency.
2. Data listing:
- The given dataset is:
[tex]\[
0, 4, 6, 8, 13, 15, 18, 22, 26, 31, 4, 6, 9, 13, 15, 19, 23, 26, 32, 1, 4, 6, 9, 14, 16, 19, 23, 27, 33,
2, 5, 7, 9, 14, 16, 20, 23, 28, 33, 2, 5, 7, 10, 14, 16, 20, 23, 28, 33, 2, 5, 7, 10, 14, 16, 20, 23, 28, 34,
3, 5, 7, 10, 15, 17, 20, 24, 29, 34, 3, 5, 8, 11, 15, 17, 20, 24, 30, 34, 3, 5, 8, 13, 15, 18, 21, 26, 30, 36,
4, 5, 8, 13, 15, 18, 21, 26, 31
\][/tex]
3. Frequency counting:
- Count how many times each number appears in the dataset.
4. Determine mode:
- Check the frequencies and determine which number appears the most.
From the counted frequencies, the number 5 appears the most frequently. Therefore:
The mode of the number of years the Supreme Court Justices served is 5.
The number of years most frequently served by the Supreme Court Justices is 5 years.
Answer: d. 5
