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
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The player with the lowest percentage increase in total runs isStudy the given table and answer the following question:
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