Bar & Pie Charts – Quantitative Aptitude Study Notes
Program: Red Hat RHCE
Topic: Bar & Pie Charts
1. Simple Explanation
| Chart Type | What It Shows | When to Use |
|---|---|---|
| Bar Chart | Discrete quantities (e.g., sales per month, number of students per class). | When comparing a few distinct categories. |
| Pie Chart | Parts of a whole, expressed as percentages or fractions (e.g., market share, budget allocation). | When you want to show how a total is divided among a few sections. |
Key Idea:
- Bar charts compare amounts directly.
- Pie charts show relative proportions of a single total.
2. Key Points
| Feature | Bar Chart | Pie Chart |
|---|---|---|
| Data type | Quantitative, discrete or grouped | Quantitative, part‑of‑whole |
| X‑axis | Category labels | Not needed (each slice is a category) |
| Y‑axis | Value or frequency | Not needed (slice size reflects proportion) |
| Reading values | Length of bar = value | Angle or arc length = proportion (percentage) |
| Calculations | Add, subtract, average, compare | Convert percentages → fractions → total |
| Common mistakes | Mis‑reading scales, omitted zero on Y‑axis | Over‑splitting slices, not summing to 100 % |
| Use in exams | “Which category has the highest/lowest value?” | “What percent belongs to X?” or “Which slice is largest?” |
Important Formulae
| Purpose | Formula |
|---|---|
| Percentage of a slice | ( \text{Percentage} = \frac{\text{Value of slice}}{\text{Total value}} \times 100 ) |
| Value of a slice from percentage | ( \text{Value} = \frac{\text{Percentage} \times \text{Total}}{100} ) |
| Comparing two bars | Compare lengths or calculate difference: ( |
| Average value of bars | ( \text{Average} = \frac{\sum \text{Bar values}}{\text{Number of bars}} ) |
3. Worked Example – Bar Chart
Problem
A company’s quarterly sales (in ₹ lakhs) are shown below. Determine:
- Which quarter had the highest sales?
- What is the total sales for the year?
- What is the average sales per quarter?
Quarter | Sales (₹ lakhs)
------------------------
Q1 | 75
Q2 | 82
Q3 | 68
Q4 | 90
Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Highest sales | Compare values | Q4 (₹ 90 lakhs) |
| 2. Total sales | (75+82+68+90 = 315) | ₹ 315 lakhs |
| 3. Average per quarter | ( \frac{315}{4} = 78.75) | ₹ 78.75 lakhs |
Answer
- Highest sales: Q4.
- Total annual sales: ₹ 315 lakhs.
- Average quarterly sales: ₹ 78.75 lakhs.
4. Worked Example – Pie Chart
Problem
A student’s annual exam marks are distributed as follows (in percentages):
- Mathematics: 35%
- Physics: 25%
- Chemistry: 20%
- Biology: 10%
- Computer Science: 10%
The total marks available are 500.
Answer:
- What is the mark obtained in each subject?
- What is the mark for the subject with the largest share?
Solution
| Subject | Percentage | Mark = ( \frac{P}{100}\times 500 ) |
|---|---|---|
| Mathematics | 35% | (0.35\times500 = 175) |
| Physics | 25% | (0.25\times500 = 125) |
| Chemistry | 20% | (0.20\times500 = 100) |
| Biology | 10% | (0.10\times500 = 50) |
| Computer Science | 10% | (0.10\times500 = 50) |
Answers
- Marks per subject:
- Math: 175
- Physics: 125
- Chemistry: 100
- Biology: 50
- CS: 50
- Largest share: Mathematics (175 marks).
5. Quick Revision Summary
-
Bar Chart
- Use for comparing discrete categories.
- Read values from bar length (Y‑axis).
- Key calculations: sum, difference, average.
-
Pie Chart
- Use for showing part‑of‑whole relationships.
- Read percentages from slice angles or labels.
- Convert between % and actual values using total.
-
Common Tips
- Always check the Y‑axis starts at zero for bar charts.
- Verify that pie chart percentages sum to 100 %.
- When total isn’t given, use the sum of all slices to infer it.
- For quick mental checks:
- If two slices add to 50 %, each is 25 % of the whole.
- 10 % of a number is 1/10 of it; 25 % is 1/4.
Mini‑Quiz (Optional)
-
A bar chart shows the number of books sold per month. The bar for “March” is 3 cm tall, while the Y‑axis increments of 1 cm represent 10 books. How many books were sold in March?
Answer: (3 \text{ cm} \times 10 = 30) books. -
In a pie chart, the