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 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:
| Program | Failed in both tests | Failed mid, Passed end | Passed mid, Failed end | Passed both tests | Total Students |
|---|---|---|---|---|---|
| B.A. | 28 | 14 | 6 | 64 | $28 + 14 + 6 + 64 = 112$ |
| B.Sc. | 23 | 12 | 17 | 55 | $23 + 12 + 17 + 55 = 107$ |
| B.Com. | 17 | 8 | 9 | 46 | $17 + 8 + 9 + 46 = 80$ |
| B.B.A. | 27 | 13 | 15 | 76 | $27 + 13 + 15 + 76 = 131$ |
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.
Important Questions from Data Interpretation
- What is the key advantage of using Geographic Information Systems (GIS) in disaster research?
- What will be the total area of land (million ha) of which 12% area is prone to flood and river erosion ?
The total runs scored by four cricketers P, Q, R, and S in years $2009$ and $2010$ are given in the following table:
Player $2009$ $2010$ P $802$ $1008$ Q $765$ $912$ R $429$ $619$ S $501$ $701$
The player with the lowest percentage increase in total runs isStudy the given table and answer the following question:
Annual consumption (in hundred tonnes) of tea in five states (A, B, C, D and E) across 6 years (2014 to 2019):State Year A B C D E 2014 112 130 136 105 117 2015 122 138 150 140 120 2016 124 134 142 144 132 2017 132 154 198 149 133 2018 135 148 187 151 145 2019 153 136 198 150 187 The total consumption of tea in state C in 2015 to 2017 is by what percentage more than the total consumption of tea in states A, B and D in 2015?
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?
