Bar & Pie Charts – Quick Study Notes
(For LIC AAO – Quantitative Aptitude)
Goal of the chapter
• Interpret data presented in bar and pie charts.
• Convert chart information into numerical values (percentages, ratios, differences).
• Solve word problems that demand quick mental calculations.
1. Simple Explanation
| Chart Type | What it shows | How to read it |
|---|---|---|
| Bar Chart | Quantitative data in discrete categories (e.g. sales of 5 products). | Compare the heights (or lengths) of bars to determine larger, smaller, or equal values. |
| Pie Chart | Proportional data that together form 100 %. | Each slice’s area is proportional to the data value. A 30 % slice occupies 30 % of the circle. |
Key Idea
- Bar → Absolute values (use heights).
- Pie → Relative percentages (use area fractions).
2. Key Points to Remember
| Bar Charts | Pie Charts |
|---|---|
| 1. Labeling – Each bar must have a clear category label. 2. Uniform Scale – Heights are on the same scale; no distortion. 3. Comparison – “Which bar is higher?” “By how many units is X larger than Y?” 4. Sum – Total of all bars may be given or required. |
1. Total = 100 % – All slices add up to 100 %. 2. Slice Size – Expressed in % or as a fraction of a whole. 3. Missing Slice – If one slice is unknown, find it by subtracting the given percentages from 100 %. 4. Finding Value – If the total value is known, multiply the percentage by the total. |
| Common Questions | Common Questions |
| • Which category has the highest/lowest value? | • What percent of the pie does a slice represent? |
| • By how many units is one bar larger than another? | • What is the value of an unknown slice? |
| • What is the sum of certain bars? | • How many parts should the pie be divided into if each part is 12 %? |
| • What fraction of the total is a specific bar? | • If a slice is 25 %, what is its 1/4 value? |
3. Worked Example
3.1 Bar Chart Example
| City | Number of Buses (in thousands) |
|---|---|
| A | 12 |
| B | 18 |
| C | 9 |
| D | 15 |
| E | 21 |
Questions
- Which city has the most buses?
- City D has 6 k fewer buses than City B. Verify.
- What percentage of the total buses are in City E?
- If the total number of buses in all cities is 75 k, does the chart match?
Solution
- Most → Highest bar → City E (21 k).
- Difference → 18 k – 15 k = 3 k (not 6 k). Answer: The statement is false.
- Percentage
[ \text{Percentage}_{E} = \frac{21}{75}\times 100 \approx 28% ] - Check Sum
[ 12+18+9+15+21 = 75,\text{k} ] ✔️ Chart is consistent.
3.2 Pie Chart Example
A company’s annual budget (₹ 1,200 000) is divided into 4 major departments:
• Marketing – 25 %
• Operations – 35 %
• Research – 15 %
• Administration – ?
Questions
- What is the missing percentage for Administration?
- How much money is allocated to Administration?
- If Research receives ₹ 180 000, confirm its percentage.
Solution
- Missing %
[ 100% - (25+35+15)% = 25% ] - Monetary value
[ 25% \times 1,200,000 = 0.25 \times 1,200,000 = 300,000 ] - Check Research
[ \frac{180,000}{1,200,000}\times 100 = 15% ] ✔️ Consistent.
4. Quick Revision Summary
| Concept | Bar Charts | Pie Charts |
|---|---|---|
| What is shown | Absolute counts per category | Proportional slices of a whole |
| Key operation | Compare bar heights; find differences; sum | Add percentages to 100 %; find missing slice; calculate value from % |
| Typical question | Which bar is tallest? | What percent does a slice represent? |
| Formula | Difference = | Bar X |
| Quick tip | If a bar is twice another, the ratio is 2 : 1. | If a slice is 1/4 of the pie, its % = 25 %. |
| Common pitfalls | Forgetting the scale; mixing up “units |