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 Program Failure Rates
The task is to identify the college program exhibiting the highest failure rate specifically for the mid-semester test.
Calculate Mid-Semester Failure Rate Formula
The failure rate is determined by the proportion of students who failed the mid-semester test out of the total students in that program. The formula is:
$ \text{Mid-Semester Failure Rate} = \left( \frac{\text{Number of students who failed mid-semester}}{\text{Total number of students in the program}} \right) \times 100\% $
Identify Students Failing Mid-Semester
Students considered to have failed the mid-semester test are those recorded in the following two categories from the table:
- Failed in both tests.
- Failed in the mid-semester test but passed in the end-semester test.
Calculate Total Students per Program
First, determine the total number of students enrolled in each program by summing up all category counts:
- B.A. Total: $28 + 14 + 6 + 64 = 112$ students
- B.Sc. Total: $23 + 12 + 17 + 55 = 107$ students
- B.Com. Total: $17 + 8 + 9 + 46 = 80$ students
- B.B.A. Total: $27 + 13 + 15 + 76 = 131$ students
Calculate Failure Numbers and Rates
Next, calculate the number of students who failed the mid-semester test for each program and then compute their respective failure rates:
| Program | Students Failing Mid-Semester | Total Students | Mid-Semester Failure Rate (%) |
|---|---|---|---|
| B.A. | $28 + 14 = 42$ | $112$ | $ \left( \frac{42}{112} \right) \times 100\% = 37.5\% $ |
| B.Sc. | $23 + 12 = 35$ | $107$ | $ \left( \frac{35}{107} \right) \times 100\% \approx 32.71\% $ |
| B.Com. | $17 + 8 = 25$ | $80$ | $ \left( \frac{25}{80} \right) \times 100\% = 31.25\% $ |
| B.B.A. | $27 + 13 = 40$ | $131$ | $ \left( \frac{40}{131} \right) \times 100\% \approx 30.53\% $ |
Determine Highest Failure Rate Program
By comparing the mid-semester failure rates calculated for each program:
- B.A.: $37.5\%$
- B.Sc.: $\approx 32.71\%$
- B.Com.: $31.25\%$
- B.B.A.: $\approx 30.53\%$
The B.A. program shows the highest failure rate in the mid-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?
