Bar & Pie Charts – Quick Study Notes
(Puducherry TET – Quantitative Aptitude)
1. Simple Explanation
| Chart | What it shows | When to use |
|---|---|---|
| Bar Chart | Quantities of different categories, absolute values | Comparing a few (≤10) items, showing increases/decreases |
| Pie Chart | Proportion of each part to a whole, percentage | When you need to show how a total is divided into parts |
Both are visual tools that make numerical data easy to understand at a glance.
2. Key Points
2.1 Bar Charts
| Feature | Details |
|---|---|
| Axes | Vertical axis → numeric scale (units), Horizontal axis → categories |
| Bar Width | Equal for all bars; spacing is important for clarity |
| Bar Height | Proportional to the value. If the axis starts at 0, heights are straight‑up. |
| Labels | Category names on x‑axis, numeric values on y‑axis or above bars |
| Common Questions | • Which category has the largest value? • What is the difference between two bars? • What is the average value? • If a new bar is added, will it change the trend? |
| Reading a Bar Chart | 1. Identify the categories. 2. Read the height from the axis. 3. Compare heights. |
| Construction Tips | • Use a clean, straight line for the axis. • Keep the scale uniform (e.g., increments of 10). • Avoid 3‑D or glitter bars. |
2.2 Pie Charts
| Feature | Details |
|---|---|
| Whole | The circle represents 100 % of the data. |
| Slices | Each slice’s angle is proportional to the part’s percentage. |
| Angle Formula | (\text{Angle} = \frac{\text{Part Value}}{\text{Total}} \times 360^\circ) |
| Labels | Either percentage or actual value inside/next to each slice. |
| Common Questions | • What is the percentage of a slice? • Which slice is the largest/smallest? • If two slices are combined, what is the new percentage? • What would be the angle of a slice if its value changes? |
| Reading a Pie Chart | 1. Note the total (100 %). 2. Read the percentage of each slice. 3. Compare proportions. |
| Construction Tips | • Keep the circle perfectly round. • Use distinct colours or shading. • Avoid overlapping slices. • For small percentages, consider labeling “<5 %” to avoid clutter. |
3. Worked Example
Problem
A company sells 4 products in a month.
| Product | Units Sold |
|---|---|
| A | 120 |
| B | 180 |
| C | 90 |
| D | 210 |
- Create a bar chart of the units sold.
- Create a pie chart showing the market share of each product (percentage of total units).
- Answer: Which product has the largest market share?
Solution
3.1 Totals & Percentages
Total units = 120 + 180 + 90 + 210 = 600
| Product | Percentage |
|---|---|
| A | (120/600 \times 100 = 20%) |
| B | (180/600 \times 100 = 30%) |
| C | (90/600 \times 100 = 15%) |
| D | (210/600 \times 100 = 35%) |
3.2 Bar Chart
- Y‑axis: Units (0 to 250, step 50).
- X‑axis: Products A, B, C, D.
- Bars:
- A → 120 (height 120).
- B → 180.
- C → 90.
- D → 210.
Interpretation: D’s bar is highest, followed by B, A, C.
3.3 Pie Chart
- Angles:
- A: (20% \times 360^\circ = 72^\circ)
- B: (108^\circ)
- C: (54^\circ)
- D: (126^\circ)
Result: D has the largest slice (35 %).
3.4 Answer
Product D has the largest market share (35 %).
4. Quick Revision Summary
-
Bar Chart
- Purpose: Compare absolute values of discrete categories.
- Read: Height ↔ value; compare heights.
- Common Queries: Largest, difference, average, trend.
- Construction: Straight axes, equal bars, clear labels.
-
Pie Chart
- Purpose: Show parts of a whole (percentages).
- Read: Slice size ↔ percentage; sum of all slices = 100 %.
- Common Queries: Largest/smallest slice, combined percentages, slice angles.
- Construction: Perfect circle, distinct colours, labels.
-
Formulas
- Pie Slice Angle: (\displaystyle \frac{\text{Part}}{\text{Total}}\times360^\circ)
- Pie Percentage: (\displaystyle \frac{\text{Part}}{\text{Total}}\times100%)
-
Tips for TET
- Always check that the total equals 100 % in pie charts.
- For bar charts, look for the highest bar; often the answer to “most” questions.