Number of students in different academic programs of a college are provided year-wise.Year Number of students admitted in different programs B.A. B.Sc. B.B.A. B. Com. B.C.A 2021 150 25 50 45 75 2022 225 40 45 62 70 2023 450 65 30 90 73 2024 470 73 35 105 70 2025 500 80 36 132 74
Analyzing College Admission Data
The question asks to identify the number of years where the number of students admitted to the B.A. program is greater than 50% of the total number of students admitted across all programs in that year.
Student Admissions Data
| Year | B.A. | B.Sc. | B.B.A. | B. Com. | B.C.A. |
|---|---|---|---|---|---|
| 2021 | 150 | 25 | 50 | 45 | 75 |
| 2022 | 225 | 40 | 45 | 62 | 70 |
| 2023 | 450 | 65 | 30 | 90 | 32 |
| 2024 | 470 | 73 | 35 | 105 | 70 |
| 2025 | 500 | 80 | 36 | 132 | 74 |
Calculating Years: B.A. vs. 50% Total
We need to perform calculations for each year:
- Calculate the total number of students admitted.
- Calculate 50% of the total students.
- Compare this 50% value with the number of B.A. students.
- Count the years where B.A. students > 50% of Total students.
Year-wise Analysis
Year 2021
- Total Students = 150 + 25 + 50 + 45 + 75 = 345
- 50% of Total Students = $\frac{345}{2}$ = 172.5
- B.A. Students = 150
- Comparison: Is 150 > 172.5? No.
Year 2022
- Total Students = 225 + 40 + 45 + 62 + 70 = 442
- 50% of Total Students = $\frac{442}{2}$ = 221
- B.A. Students = 225
- Comparison: Is 225 > 221? Yes. (Count = 1)
Year 2023
- Total Students = 450 + 65 + 30 + 90 + 32 = 667
- 50% of Total Students = $\frac{667}{2}$ = 333.5
- B.A. Students = 450
- Comparison: Is 450 > 333.5? Yes. (Count = 2)
Year 2024
- Total Students = 470 + 73 + 35 + 105 + 70 = 753
- 50% of Total Students = $\frac{753}{2}$ = 376.5
- B.A. Students = 470
- Comparison: Is 470 > 376.5? Yes. (Count = 3)
Year 2025
- Total Students = 500 + 80 + 36 + 132 + 74 = 822
- 50% of Total Students = $\frac{822}{2}$ = 411
- B.A. Students = 500
- Comparison: Is 500 > 411? Yes. (Count = 4)
Final Result
The condition (B.A. students > 50% of Total students) is met in 4 years (2022, 2023, 2024, 2025).
Important Questions from Data Interpretation
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