A college has four programs B.A., B.Sc., B.Com. and B.B.A. The results of the mid-semester and end-semester tests are shown in the table given below.Results Number of students Β.Α. B.Sc. B.Com. Β.Β.Α. Failed in both tests 28 23 17 27 Failed in mid-semester test but passed in end-semester test 14 12 8 13 passed in mid-semester test but failed in end-semester test 6 17 9 15 Passed in both tests 64 55 46 76
Analyze End-Semester Test Results
To find the program with the lowest passing percentage in the end-semester test, we first need to calculate the total number of students and the number of students who passed the end-semester test for each program.
Students who passed the end-semester test include those who:
- Failed in the mid-semester test but passed in the end-semester test.
- Passed in both tests.
The total number of students in a program is the sum of students in all four categories.
Summarize Student Data
The following table summarizes the data provided:
| Program | Failed in both tests | Failed mid, Passed end | Passed mid, Failed end | Passed both tests | Total Students |
|---|---|---|---|---|---|
| B.A. | 28 | 14 | 6 | 64 | $28 + 14 + 6 + 64 = 112$ |
| B.Sc. | 23 | 12 | 17 | 55 | $23 + 12 + 17 + 55 = 107$ |
| B.Com. | 17 | 8 | 9 | 46 | $17 + 8 + 9 + 46 = 80$ |
| B.B.A. | 27 | 13 | 15 | 76 | $27 + 13 + 15 + 76 = 131$ |
Calculate End-Semester Passing Percentages
The passing percentage for the end-semester test is calculated using the formula:
$ \text{Passing Percentage} = \left( \frac{\text{Number of students who passed end-semester}}{\text{Total number of students}} \right) \times 100 $
B.A. Program
- Students passed end-semester: $14 + 64 = 78$
- Total students: $112$
- Passing percentage: $ \left( \frac{78}{112} \right) \times 100 \approx 69.64\% $
B.Sc. Program
- Students passed end-semester: $12 + 55 = 67$
- Total students: $107$
- Passing percentage: $ \left( \frac{67}{107} \right) \times 100 \approx 62.62\% $
B.Com. Program
- Students passed end-semester: $8 + 46 = 54$
- Total students: $80$
- Passing percentage: $ \left( \frac{54}{80} \right) \times 100 = 67.5\% $
B.B.A. Program
- Students passed end-semester: $13 + 76 = 89$
- Total students: $131$
- Passing percentage: $ \left( \frac{89}{131} \right) \times 100 \approx 67.94\% $
Determine Lowest Passing Percentage
Comparing the passing percentages:
- B.A.: $ \approx 69.64\% $
- B.Sc.: $ \approx 62.62\% $
- B.Com.: $ 67.5\% $
- B.B.A.: $ \approx 67.94\% $
The B.Sc. program has the lowest passing percentage in the end-semester test.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 Who had the best score on either test?
Who had the most consistent scores on both tests?
Who had the least consistent scores on both tests?
Who had the poorest score on either test?
