Explanation:
The question states that a small mid-western town has a high level of juvenile delinquency and a large number of children dropping out of schools. However, it is surprising to note that the town also has one of the highest numbers of precocious youngsters in the country.

Definition of precocious:
Precocious means having developed certain abilities or talents at an earlier age than usual. In the context of the question, it refers to youngsters who display advanced skills, intelligence, or maturity at a young age.

Supporting Analysis:
1. Contrast: The question establishes a contrast by pointing out the high level of juvenile delinquency and school dropouts in the town. This suggests that the town might not have a favorable environment for the development of children.
2. Surprising fact: The question states that despite the unfavorable circumstances, the town has one of the highest numbers of precocious youngsters in the country. This fact is unexpected and needs an explanation.

Possible Explanation:
1. Challenges and Adversity: The unfavorable circumstances in the town, such as high juvenile delinquency and school dropouts, might have created a challenging environment. In such situations, some children may develop resilience and determination to overcome obstacles, leading to their precocious development.
2. Limited Opportunities: The limited opportunities for personal growth and development in the town might have motivated some children to seek alternative ways to learn and excel. They may have taken the initiative to explore their interests, acquire knowledge independently, and develop advanced skills.
3. Supportive Community: Despite the challenges, the town might have a supportive community that recognizes and encourages the potential of young individuals. This support could include mentorship programs, extracurricular activities, or access to resources that foster talent and intellectual growth.
4. Individual Motivation: Some youngsters may have intrinsic motivation and a strong desire to succeed, which can drive them to develop their abilities at a young age. This internal drive might be fueled by personal goals, aspirations, or role models who have achieved success despite similar circumstances.

Conclusion:
In summary, the small mid-western town's high level of juvenile delinquency and school dropouts may be surprising, but the presence of a significant number of precocious youngsters suggests that despite the challenges, some individuals have managed to overcome adversity and develop advanced skills, intelligence, or maturity at a young age.