Model Answer
0 min readIntroduction
The concept of financial aid in educational institutions is often linked to socio-economic factors and merit. However, innovative approaches, like the one described in the question, utilize performance-based metrics – in this case, internship stipends – to determine aid allocation. This method aims to incentivize students and potentially create a self-sustaining financial aid system. Understanding the distribution of stipends is crucial for effective resource allocation and ensuring equitable access to education. This question tests the ability to apply basic statistical principles to a real-world scenario within an educational context.
Calculating the Mode
The mode represents the value that appears most frequently in a dataset. In this case, we need to identify the stipend range with the highest number of students.
| Stipend earned (in₹) | Number of students |
|---|---|
| 0 - 49,999 | 231 |
| 50,000 - 99,999 | 304 |
| 1,00,000 - 1,49,999 | 400 |
| 1,50,000 - 1,99,999 | 296 |
| 2,00,000 - 2,49,999 | 123 |
| 2,50,000 - 2,99,999 | 68 |
| 3,00,000 or more | 23 |
From the table, the stipend range of ₹1,00,000 - ₹1,49,999 has the highest number of students (400). Therefore, the mode value of the stipend earned is considered to be the midpoint of this range, which is ₹1,25,000 (average of 100000 and 149999). For practical purposes, we can consider the mode to be approximately ₹1,25,000.
Determining Financial Aid Eligibility
The financial aid is restricted to students whose stipend earnings are at least 10% lower than the mode value. First, we calculate 10% of the mode value:
10% of ₹1,25,000 = ₹12,500
Next, we subtract this amount from the mode value to find the eligibility threshold:
₹1,25,000 - ₹12,500 = ₹1,12,500
Therefore, students who earned a stipend of at least ₹1,12,500 are not eligible for financial aid. We need to count the number of students who earned less than ₹1,12,500.
Looking at the stipend distribution:
- Students earning 0 - 49,999: 231
- Students earning 50,000 - 99,999: 304
- Students earning 1,00,000 - 1,09,999: Approximately 300 (proportionately assuming uniform distribution within the 1,00,000 - 1,49,999 range)
Total number of students eligible for financial aid = 231 + 304 + 300 = 835
Conclusion
In conclusion, the mode value of the stipend earned by the students is approximately ₹1,25,000. Based on the given criteria, 835 students qualify for financial aid as their stipend earnings are at least 10% lower than the mode value. This approach to financial aid allocation, while potentially incentivizing performance, requires careful consideration of equity and potential biases. Further analysis of the distribution and student needs would be beneficial for optimizing the aid system.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.