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 given below shows the earnings of two persons on five different days.
What is the ratio of total earnings of P to the total earnings of Q?Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68 The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
Colour Total toys Percentage of cars C1 500 12 C2 600 15 C3 400 12.5 C4 550 10 C5 650 20 C6 450 10 What is the total number of car toys of C2 and C3 taken together?
Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
