Bar & Pie Charts – Quick Study Notes
Program: CDS | Subject: Quantitative Aptitude | Topic: Bar & Pie Charts
1. Simple Explanation
| Chart | What it shows | When to use |
|---|---|---|
| Bar Chart | Quantitative comparison of categories. Each category has a rectangular bar whose height (or length if horizontal) is proportional to its value. | Comparing discrete quantities (e.g., sales of 5 products, number of students in each class). |
| Pie Chart | Proportional relationship of parts to a whole. The whole circle (360°) is divided into sectors whose angles are proportional to each category’s share. | Showing how a whole is divided into parts (e.g., market share, budget distribution). |
Key Idea:
Bar chart – compare heights of bars.
Pie chart – compare slice angles or areas (usually angles are easier to read).
2. Key Points (Quick Reference)
| Feature | Bar Chart | Pie Chart |
|---|---|---|
| Data Input | Exact numeric values (e.g., 120, 75, 98). | Percentages or raw numbers (converted to %). |
| Scale | Common scale on the y‑axis (or x‑axis for horizontal). | Scale is 360° (or 100%). |
| Reading | Find “bar height” → value (or percentage if scale is in %). | Find “slice angle” → percentage (or value if total known). |
| Missing part | Add all bars → total; missing = total – sum of known bars. | Add all percentages → 100%; missing = 100% – sum of known percentages. |
| Angle–Percentage Relation | Angle(°) = (Percentage / 100) × 360 |
Percentage = (Angle(°) / 360) × 100 |
| Common Pitfalls | 1. Wrong axis scale. 2. Over‑lapping bars. 3. Ignoring gaps between bars. |
1. Forgetting that total = 360°. 2. Mis‑reading labels (e.g., 30° = 30%? No, 30° = 8.33%). 3. Assuming equal angles when percentages differ. |
3. Worked Example
Problem Statement
A company surveyed 400 employees about their preferred work‑style:
| Work‑style | Number of Employees |
|---|---|
| Remote | 120 |
| Hybrid | 200 |
| On‑site | 80 |
- Draw a bar chart for the data.
- Construct a pie chart (show the angle of each slice).
- Find the percentage of employees who prefer Hybrid work‑style.
- If the Remote slice angle is 108°, verify the data.
Step‑by‑Step Solution
1. Bar Chart
- Y‑axis: Number of employees (0 to 250, step 50).
- Bars:
- Remote: 120
- Hybrid: 200
- On‑site: 80
Interpretation: Hybrid has the tallest bar.
2. Pie Chart
- Total = 400.
- Percentages
- Remote = (120/400) × 100 = 30%
- Hybrid = (200/400) × 100 = 50%
- On‑site = (80/400) × 100 = 20%
- Angles
- Remote = 30% × 360° = 108°
- Hybrid = 50% × 360° = 180°
- On‑site = 20% × 360° = 72°
3. Percentage of Hybrid
Already computed: 50%.
4. Verify Remote Angle
- Angle of Remote slice = 108°
- Percent from angle = (108/360) × 100 = 30% → matches the data.
4. Quick Revision Summary (Bullet Points)
-
Bar Chart
- Use when you have discrete categories with exact counts.
- Read value from vertical (or horizontal) scale.
- Add all bars → total; missing part = total – sum(known).
-
Pie Chart
- Use when you need to show parts of a whole.
- Total circle = 360°.
- Convert raw numbers → percentages → angles.
Angle = (Part / Whole) × 360.Percentage = (Angle / 360) × 100.
-
Common Calculations
Task Formula Example