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 What does the height of the rectangle in a histogram show?
Following table provides figures (in rupees) on annual expenditure of a firm for two years – 2010 and 2011.
Category
2010
2011
Raw material
5200
6240
Power & fuel
7000
9450
Salary & wages
9000
12600
Plant & machinery
20000
25000
Advertising
15000
19500
Research & Development
22000
26400
In 2011, which of the following two categories have registered increase by same percentage?
Read the following table giving sales data of five types of batteries for years 2006 to 2012
Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
102
84
126
2008
96
114
75
105
135
2009
105
90
150
90
75
2010
90
75
135
75
90
2011
105
60
165
45
120
2012
115
85
160
100
145
Out of the following which type of battery achieved highest growth between the years 2006 and 2012?Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F and G?
A
D
B
G
E
C
F
