Bar & Pie Charts – Quick Study Notes
(For the Punjab Police Constable – Quantitative Aptitude)
1. Simple Explanation
| Chart | What it shows | When to use |
|---|---|---|
| Bar Chart | Quantitative data expressed as bars (vertical or horizontal). | Comparing discrete categories, showing trends over time. |
| Pie Chart | A circle divided into sectors, each sector representing a part of a whole. | Showing proportions / percentages of a total. |
Key Idea – In both charts the size (height of a bar, angle of a sector) is proportional to the value it represents.
To answer questions from a chart, you only need to read or compute that proportional size, not the whole chart itself.
2. Key Points
2.1 Bar Charts
| Item | Details |
|---|---|
| Axes | Y‑axis = value (often in units), X‑axis = categories. |
| Bar Height/Length | Directly proportional to the value. |
| Reading a Bar | 1. Locate the bar on the X‑axis. 2. Read the Y‑axis value at the top of the bar. |
| Comparisons | Taller bars = larger values. |
| Percentage from Bar | (\displaystyle \frac{\text{Bar value}}{\text{Sum of all bars}}\times 100% ) |
| Missing Value | If the sum of some bars is known, subtract from total to get missing bar. |
| Common Mistakes | – Ignoring the scale (e.g., 0–20 vs 0–200). – Misreading the axis label. |
2.2 Pie Charts
| Item | Details |
|---|---|
| Whole | 360° (full circle). |
| Sector Angle | (\displaystyle \text{Angle} = \frac{\text{Part}}{\text{Whole}}\times360^\circ) |
| Percentage | (\displaystyle \frac{\text{Part}}{\text{Whole}}\times100% ) |
| Area of Sector | (\displaystyle \text{Area} = \frac{\text{Angle}}{360^\circ}\times \pi r^2) |
| Missing Part | If all other sectors’ angles/percentages are known, subtract from 360° (or 100%). |
| Finding the Part Size | If the whole is given in units (e.g., 500 units) and the percentage is known, multiply: |
| (\displaystyle \text{Part} = \frac{\text{Percentage}}{100}\times\text{Whole}) | |
| Common Errors | – Confusing 360° with 100%. – Mis‑calculating the missing sector. |
2.3 General Tips
- Always check the scale – the Y‑axis may not start at 0.
- Use the full circle (360°) only for pie charts.
- Round Off Carefully – if a question demands the nearest integer, round after the final calculation.
- Cross‑verify – sum of all bar values should equal total, sum of all pie angles = 360°, sum of percentages = 100%.
3. Worked Example
3.1 Problem Statement
A bar chart shows the number of recruits in 5 districts (A–E) for the year 2024:
| District | Recruits |
|---|---|
| A | 120 |
| B | 200 |
| C | – |
| D | 80 |
| E | 100 |
The chart’s Y‑axis is in units of 20 (i.e., 20, 40, 60, …).
The total number of recruits is 700.
Questions
- Find the number of recruits in District C.
- In a pie chart representing the same data, what is the angle of the sector for District B?
- What percentage of the total recruits came from District D?
3.2 Solution
3.2.1 Bar Chart – Missing Value
Sum of known recruits: [ 120 + 200 + 80 + 100 = 500 ] Total recruits = 700, so [ \text{District C} = 700 - 500 = \boxed{200} ]
3.2.2 Pie Chart – Angle for District B
Percentage for District B: [ \frac{200}{700}\times100 = 28.57% ;\text{(≈ 28.6%)} ] Angle: [ \text{Angle} = 28.57%\times 360^\circ = 0.2857\times360^\circ = 102.86^\circ ;\text{(≈ 103°)} ] [ \boxed{103^\circ} ]
3.2.3 Percentage for District D
[ \frac{80}{700}\times100 = 11.43% ;\text{(≈ 11.4%)} ] [ \boxed{11.4%} ]
3.3 Quick Check
| District | Recruits | % of Total | Pie Angle (°) |
|---|---|---|---|
| A | 120 | 17.14% | 61.7° |
| B | 200 | 28.57% | 102.9° |
| C | 200 | 28.57% | 102.9° |