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:

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.