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
Program Difficulty Comparison
The objective is to identify the program with the least difficult mid-semester test. The criterion used is the number of students passing the test.
A test is considered least difficult when the highest number of students pass it. To find this, we calculate the total number of students who passed the mid-semester test for each program.
Students who passed the mid-semester test are those who either:
- Passed the mid-semester test but failed the end-semester test.
- Passed both the mid-semester and end-semester tests.
Calculate Mid-Semester Passers
From the given table, the relevant data for students passing the mid-semester test are:
| Results | B.A. | B.Sc. | B.Com. | B.B.A. |
|---|---|---|---|---|
| Passed in mid-semester test but failed in end-semester test | 6 | 17 | 9 | 15 |
| Passed in both tests | 64 | 55 | 46 | 76 |
Now, calculate the total number of students who passed the mid-semester test for each program:
- B.A.: $6 + 64 = 70$ students
- B.Sc.: $17 + 55 = 72$ students
- B.Com.: $9 + 46 = 55$ students
- B.B.A.: $15 + 76 = 91$ students
Identify Least Difficult Mid-Semester Test
Compare the number of students passing the mid-semester test across all programs:
- B.A.: 70
- B.Sc.: 72
- B.Com.: 55
- B.B.A.: 91
The B.B.A. program recorded the highest number of students (91) passing the mid-semester test. This indicates that the mid-semester test for B.B.A. was the least difficult among the programs.
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?
