Bar & Pie Charts – Quantitative Aptitude
For the Andaman & Nicobar Islands Police Constable (ANIPC) Examination
1. Simple Explanation
| Chart | What it shows | When to use |
|---|---|---|
| Bar Chart | Qualitative or quantitative data – each bar’s length (or height) represents the value of a category. | When comparing discrete categories (e.g. number of cases per month). |
| Pie Chart | Proportional data – the whole circle represents 100 % and each slice shows a part of the whole. | When you are given a part and asked to find the whole, or vice‑versa, or to compare proportions. |
Both charts are visual tools that let you estimate or exactly calculate values such as:
- Exact value of a bar or slice
- Total of all categories
- Percentage of a particular category
- Ratio of two categories
2. Key Points
| Aspect | Bar Charts | Pie Charts |
|---|---|---|
| Basic Element | Bars – height (or length) proportional to value. | Slices – angular measure proportional to percentage. |
| Scale | Usually a linear scale on the axis (e.g., 0‑10, 0‑20). | The whole circle is 360°, or 100 % (when not given). |
| Units | Can be any unit (cases, revenue, etc.). | Usually no unit; all values are relative. |
| Reading a bar | 1. Find the bar. 2. Read its length from the axis. 3. Convert if the axis is not in the required unit. | 1. Find the slice. 2. Read its angle or percentage. 3. Convert to the requested value. |
| Common Questions | - Find the value of a bar. - Find the total of all bars. - Find the percentage of a bar relative to the total. |
- Find the whole when one part and its percentage are known. - Find the part when the whole and a percentage are known. - Find the percentage of one slice relative to another. |
| Tips for Accuracy | • Always check the axis scale. • If the axis uses a unit (e.g., 5 units = 10 cases), multiply accordingly. • If the chart is drawn on paper, estimate if the scale is missing. |
• If angles are given, remember that 360° = 100 %. • Convert percentages to fractions only when necessary. • When a slice has “x %” and the whole is “y units”, the slice value = (y \times \frac{x}{100}). |
3. Bar Charts
3.1 How to Read a Bar Chart
- Identify the Category – look at the label on the x‑axis.
- Locate the Bar – the bar that corresponds to the category.
- Read the Height – use the y‑axis scale.
- Convert if Needed – apply any unit conversion given in the question.
3.2 Common Formulae
| Question | Formula | Example |
|---|---|---|
| Value of one bar | (V = \text{height on axis}) | A bar reaches 15 on the axis → 15 units. |
| Total of all bars | (T = \sum V_i) | 5 bars: 12 + 8 + 15 + 6 + 9 = 50. |
| Percentage of a bar | (% = \frac{V_{\text{bar}}}{T} \times 100) | ( \frac{15}{50} \times 100 = 30%). |
3.3 Worked Example – Bar Chart
Problem (ANIPC style)
A bar chart shows the number of theft cases recorded in a police station for the last 6 months.
- January – 20 cases
- February – 35 cases
- March – 28 cases
- April – 15 cases
- May – 30 cases
- June – 22 cases
Questions
- What is the total number of cases for the 6 months?
- What percentage of the total were recorded in March?
- Which month had the highest number of cases?
Solution
| Month | Cases |
|---|---|
| Jan | 20 |
| Feb | 35 |
| Mar | 28 |
| Apr | 15 |
| May | 30 |
| Jun | 22 |
| Total | 150 |
- Total = 20 + 35 + 28 + 15 + 30 + 22 = 150 cases.
- March = 28 cases.
[ %_{\text{Mar}} = \frac{28}{150} \times 100 \approx 18.67% ] - February has the highest value: 35 cases.
Answer
- 150 cases
- ~18.7 %
- February
4. Pie Charts
4.1 How to Read a Pie Chart
- Identify the Slice – look at the legend or label.
- Read its Angle or Percentage – either given directly or deducible