Bar & Pie Charts – Quantitative Aptitude
(Tamil Nadu Police Constable Exam – Quantitative Aptitude)
1. Simple Explanation
| Chart | What it shows | When to use | Key feature |
|---|---|---|---|
| Bar Chart | Quantity of individual categories | Discrete data (e.g. number of crimes per month, number of officers per station) | Bars are rectangular; length/height represents magnitude |
| Pie Chart | Proportion of a whole | Categorical data that adds up to 100 % (e.g. percentage of crime types) | One circle; each slice’s angle is proportional to its share |
- Bar charts are best when you need to compare individual values.
- Pie charts are best when you want to see relative shares of a whole.
2. Key Points to Remember
| # | Point | Why it matters |
|---|---|---|
| 1. Axis & Scale | Bar chart always has a horizontal or vertical axis; keep scale uniform (e.g., 0‑10 k). | Prevents visual distortion. |
| 2. Ordering | For bar charts, order categories logically (time, increasing value, alphabetically). | Easier comparison. |
| 3. Bar width & spacing | Keep width equal; spacing uniform. | Improves readability. |
| 4. Calculating percentages | (\text{percentage} = \frac{\text{part}}{\text{total}}\times 100%) | Needed for pie charts or converting bar data. |
| 5. Missing values | If one bar is missing, find total first (often given) and subtract known values. | Common exam trick. |
| 6. Ratio & proportion | Compare two bars directly: (\frac{A}{B}) or (\frac{A}{\text{total}}). | Quick mental comparison. |
| 7. Pie slice angle | ( \text{Angle} = \frac{\text{percentage}}{100}\times 360^\circ). | Useful if you’re asked to find missing slice. |
| 8. Check that pie sums to 100 % | A mistake in percentages will break the chart. | Validate before answering. |
| 9. Approximate values | If numbers are large, use “rounded” percentages (e.g., 27 % ≈ 30 %) for mental math. | Saves time. |
| 10. Labeling | Write category names and values clearly. | Avoid misreading. |
3. Worked Example
Scenario
The Tamil Nadu Police Department recorded the monthly number of theft cases in January–June 2023.
A bar chart is given (see below). The chart shows:
| Month | Theft Cases |
|---|---|
| Jan | 128 |
| Feb | 145 |
| Mar | 119 |
| Apr | 137 |
| May | 134 |
| Jun | missing |
The total number of theft cases in the first six months is 815 (given on the chart).
Tasks
- Find the missing value for June.
- Create a pie chart showing the share of each month.
- Determine which month had the highest share of total thefts.
Step‑by‑Step Solution
1. Missing value (June)
[ \text{June} = \text{Total} - (\text{Jan}+\text{Feb}+\text{Mar}+\text{Apr}+\text{May}) ]
[ \text{June} = 815 - (128+145+119+137+134) = 815 - 663 = 152 ]
June = 152 cases.
2. Calculate percentages for each month
[ \text{Percentage} = \frac{\text{Month cases}}{815}\times 100 ]
| Month | Cases | Percentage (rounded) |
|---|---|---|
| Jan | 128 | ( \frac{128}{815}\times100 \approx 15.7% ) → 16 % |
| Feb | 145 | ( \approx 17.8% ) → 18 % |
| Mar | 119 | ( \approx 14.6% ) → 15 % |
| Apr | 137 | ( \approx 16.8% ) → 17 % |
| May | 134 | ( \approx 16.4% ) → 16 % |
| Jun | 152 | ( \approx 18.6% ) → 19 % |
(Rounded to nearest whole number for pie slices.)
3. Draw the pie chart
- Sum of rounded percentages = 16 + 18 + 15 + 17 + 16 + 19 = 101 % (slight rounding error; acceptable in exam context).
- Convert percentages to angles:
[ \text{Angle} = \frac{\text{Percentage}}{100}\times360^\circ ]
| Month | Angle (°) |
|---|---|
| Jan | (16%\times360 = 57.6^\circ) |
| Feb | (18%\times360 = 64.8^\circ) |
| Mar | (15%\times360 = 54^\circ\ |