Final answer:
The mode for the given set of age data is 74 because the number 4 as a leaf appears most frequently in the dataset. Therefore, from the provided options, the correct answer is (a) 4.
Step-by-step explanation:
The question asks to find the mode for the given set of age data represented in a stem-and-leaf plot. To identify the mode, we need to determine which age appears most frequently in the dataset. Examining the stem-and-leaf plot:
- 50s - Stem: 4 | Leaves: 6
- 60s - Stem: 6 | Leaves: 2, 3, 4, 8, 8
- 70s - Stem: 7 | Leaves: 2, 3, 4, 4, 4, 8
- 80s - Stem: 8 | Leaves: 4, 5, 6, 8
We see that the number 4 (specifically 74) appears the most frequently as a leaf value, with 74 occurring three times. Therefore, the mode of this dataset is 74.
Since the question provides choices represented by the last digit of the ages, the correct answer from the choices given is option (a) 4.