Bar & Pie Charts
(Quantitative Aptitude – Gujarat Police Sub‑Inspector (SI) Exam)
Purpose of these notes – Quickly understand what bar & pie charts are, how to read and construct them, and how to solve typical exam problems.
1. Simple Explanation
| Chart | What it shows | Best for | Key visual element |
|---|---|---|---|
| Bar chart | Quantitative values of discrete categories | Comparing magnitudes, trends, or distributions | Length of bars (horizontal or vertical) |
| Pie chart | Proportional parts of a whole | Quick snapshot of relative shares | Angles (or arc lengths) of slices |
- Bar chart: Each bar’s height (or width) is proportional to the value it represents.
- Pie chart: The whole circle represents 100 %. Each slice’s angle/arc is proportional to its percentage share.
2. Key Points to Remember
| Aspect | Bar Charts | Pie Charts |
|---|---|---|
| Data type | Discrete (e.g., number of cases, sales) | Categorical proportions of a whole |
| Units | Same unit for all bars (e.g., rupees, count) | Percent or fraction of total |
| Axis | X‑axis = categories, Y‑axis = value | No axes – just the circle |
| Interpretation | Compare bar lengths to see largest/smallest, trends over time | Compare slice angles to see largest share, compute percentage |
| Common questions | 1. Which category has the largest value? 2. What is the value of a missing bar? 3. Rate of change between two bars | 1. What percent does a slice represent? 2. Find missing percentage. 3. Find actual value from a given percentage |
| Calculations | Use ratios: value = (bar length / scale) × unit. |
Use proportions: percentage = (slice angle / 360°) × 100. |
| Total check | Sum of all bars should equal the total (if given). | Sum of all percentages must equal 100 %. |
3. Worked Example
3.1 Bar Chart Example
Problem
A bar chart shows the number of cases reported in a police station during four months.
- January: 18 cases
- February: 24 cases
- March: 12 cases
- April: 30 cases
Questions
- Which month had the highest number of cases?
- What is the average number of cases per month?
- If the total cases for the quarter (Jan–Mar) are required, what is it?
Solution
| Month | Cases |
|---|---|
| Jan | 18 |
| Feb | 24 |
| Mar | 12 |
| Apr | 30 |
- Highest – April (30).
- Average – ((18 + 24 + 12 + 30)/4 = 84/4 = 21) cases.
- Quarterly Jan–Mar – (18 + 24 + 12 = 54) cases.
(In a bar chart you would look at the tallest bar, count the height, and add the bar heights for totals.)
3.2 Pie Chart Example
Problem
A pie chart shows the distribution of traffic violations in a city:
| Category | Percentage |
|---|---|
| Speeding | 40 % |
| Illegal Parking | 30 % |
| Driving without a helmet | ? |
| Others | 10 % |
The total of all categories must be 100 %.
Questions
- What is the missing percentage for “Driving without a helmet”?
- If the total number of violations recorded is 2,500, how many were “Driving without a helmet”?
Solution
-
Missing percentage
[ 100% - (40% + 30% + 10%) = 100% - 80% = 20% ] So, Driving without a helmet = 20 %. -
Actual number
[ \text{Number} = \frac{\text{percentage}}{100}\times \text{total} = \frac{20}{100}\times 2500 = 0.20\times 2500 = 500 ] So, 500 violations were for “Driving without a helmet”.
(In a pie chart you would draw the circle, compute the missing slice so that the whole circle makes 360°, and then use the percentage to find the actual count.)
4. Quick Revision Summary
| Topic | What to remember |
|---|---|
| Bar Chart | • Bars proportional to values • Highest = tallest bar • Sum of bars = total (if required) • Compute averages, differences, growth |
| Pie Chart | • Whole = 100 % or 360° • Slice angle ∝ percentage • Missing percentage = 100 % - sum of known percentages • Actual count = (percentage/100) × total |
| Common Formulas | - value = (bar length / scale) × unit- percentage = (slice angle / 360°) × 100- actual count = (percentage/100) × total |
| Checkpoints | • Verify that all percentages add to 100 % in pie charts. • Verify that all bar lengths are on the same scale. • Re‑calculate totals for consistency. |
| Exam Tip | When a question asks for “percentage of the whole” relative to a bar chart, first convert the bar value into a percentage of the total (sum of all bars). |
Practice Problems (For Self‑Study)
- Bar Chart
A police station records the following number of theft cases per week:
Week 1: 12, Week 2: 18, Week 3: 15, Week 4: 9.- Which week had the fewest cases?
- What is the total number of cases in the month?
- If the average per week is required