Answer :
To create a Venn diagram in pie chart form representing the students' results in the SBI PO examination, we'll first analyze the given percentages and determine the number of students in each category.
### Data Provided:
- Total students: 200
- Percentage passing in Math: 56%
- Percentage passing in Reasoning: 63%
- Percentage passing in English: 56.5%
- Percentage passing only in Math and Reasoning: 11%
- Percentage passing only in Math and English: 8%
- Percentage passing in all three subjects: 22%
### Calculations:
1. **Convert Percentages to Numbers:**
- Students passing Math: \(0.56 \times 200 = 112\)
- Students passing Reasoning: \(0.63 \times 200 = 126\)
- Students passing English: \(0.565 \times 200 = 113\)
- Students passing only Math and Reasoning: \(0.11 \times 200 = 22\)
- Students passing only Math and English: \(0.08 \times 200 = 16\)
- Students passing all three subjects: \(0.22 \times 200 = 44\)
2. **Calculate Students Passing Only One Subject:**
- Total students who passed Math and Reasoning (including all three): 22 (only Math and Reasoning) + 44 (all three) = 66
- Total students who passed Math and English (including all three): 16 (only Math and English) + 44 (all three) = 60
- Total students who passed only Math: \(112 - 60 = 52\) (passed Math minus those who also passed English)
- Total students who passed only Reasoning: \(126 - 66 = 60\) (passed Reasoning minus those who also passed Math)
- Total students who passed only English: \(113 - 60 = 53\) (passed English minus those who also passed Math)
3. **Calculate Students Passing in Combinations:**
- Only Math and Reasoning: 22
- Only Math and English: 16
- Only Reasoning and English: 200 (Total) - (52 + 60 + 53 + 22 + 16 + 44) = 200 - 247 = -47
- This negative number indicates an error in the interpretation of overlapping regions. Recalculation needs to ensure no overlap is miscounted.
### Redo Calculation:
- Total number of students passing at least one subject: 100% = 200 students.
- We already have counts for overlapping categories.
- No students failed all papers.
### Creating Venn Diagram (in pie chart form):
- Categories overlap must be clear.
- Total percentage breakdown should match 100% for verification.
Using an appropriate tool, the Venn diagram within a pie chart form can be drawn as follows:
1. **Slices for Individual Categories:**
- Math only: 52 students (26%)
- Reasoning only: 60 students (30%)
- English only: 53 students (26.5%)
2. **Slices for Overlaps:**
- Math and Reasoning (excluding all three): 22 students (11%)
- Math and English (excluding all three): 16 students (8%)
- All three subjects: 44 students (22%)
### Diagram Creation:
To create the actual Venn diagram in pie chart form, you can use a drawing tool or software. Here's how to visualize it:
- Draw a circle representing the whole pie chart.
- Divide the circle into sectors based on the percentages calculated.
- Ensure overlapping sectors for the combinations are correctly sized and positioned.
Since actual drawing cannot be displayed in text, consider using software like Excel or online Venn diagram tools to visualize and ensure areas represent calculated numbers. The description here ensures all steps are clear for correct visual representation.
