Bar & pie charts: Quantitative Aptitude Notes for Lakshadweep Police Constable

Bar & Pie Charts – Quantitative Aptitude

(Lakshadweep Police Constable – Quantitative Aptitude)

Goal:
Understand how to read, interpret and solve problems involving bar charts and pie charts.

1. Simple Explanation

Chart	What it shows	When to use it
Bar Chart	Frequency / count of discrete categories (e.g., number of complaints per month).	When you have distinct categories and need to compare their magnitudes.
Pie Chart	Part‑of‑whole relationship (percentage of total).	When you need to show how a whole is divided into parts.

Key Idea

Bar chart → Absolute values (counts, amounts).
Pie chart → Relative values (percentages, fractions of 100 % or 360°).

2. Key Points

Feature	Bar Chart	Pie Chart
Units	Can be any quantity (units, people, money).	Always expressed in percent or degrees (sum = 100 % or 360°).
Shape	Rectangles (bars) – height (or length) ∝ value.	Sectors of a circle – angle ∝ value.
Data source	Raw counts or frequencies.	Derived from raw data by converting to percentages.
Reading	Find the bar’s height (or read the axis).	Find the angle or read the percentage label.
Common mistakes	Confusing bars of equal length with equal value (axis may be scaled).	Mis‑reading percentages that do not add up to 100 %.
Applications	Comparing sales of products, number of cases of disease, etc.	Market share, budget allocation, population distribution.

Quick Calculation Rules

Situation	Formula
Total of a pie chart	Sum of all percentages = 100 % (or 360°).
Percentage from raw data	(\displaystyle % = \frac{\text{part}}{\text{whole}}\times 100)
Angle of a pie sector	(\displaystyle \theta = \frac{\text{part}}{\text{whole}}\times 360^\circ)
Value from a bar chart	Count on the axis or labelled directly.

3. Worked Example

Problem

A police station recorded the number of complaints received in a week as follows:

Category	Complaints
Theft	48
Assault	27
Vandalism	35
Others	10

Draw a bar chart.
Create a pie chart.
Find the percentage of Assault complaints.
What angle (in degrees) does the Theft sector occupy?

Solution

1. Bar Chart

          |         |         |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |   █     |   █     |
          |_________|_________|
            Theft   Assault

In practice you would draw bars of height proportional to 48, 27, 35, and 10.

2. Pie Chart

Total complaints = 48 + 27 + 35 + 10 = 120.

Category	Part	Percentage
Theft	48	(48/120 \times 100 = 40%)
Assault	27	(27/120 \times 100 = 22.5%)
Vandalism	35	(35/120 \times 100 = 29.17%)
Others	10	(10/120 \times 100 = 8.33%)

Pie sectors are drawn with angles:

Theft: (40% \times 360^\circ = 144^\circ)
Assault: (22.5% \times 360^\circ = 81^\circ)
Vandalism: (29.17% \times 360^\circ \approx 105^\circ)
Others: (8.33% \times 360^\circ \approx 30^\circ)

3. Percentage of Assault

[ \frac{27}{120}\times 100 = 22.5% ]

4. Angle for Theft

[ \theta_{\text{Theft}} = \frac{48}{120}\times 360^\circ = 144^\circ ]

4. Revision Summary (Quick Flashcards)

Topic	Question	Answer
Bar chart reading	What does the height of a bar represent?	The absolute quantity of that category.
Bar chart reading	Why must you check the axis scale?	To avoid misinterpreting bars of equal length as equal values.
Pie chart calculation	How to find the percentage of a part?	((\text{part}/\text{whole}) \times 100).
Pie chart calculation	What is the sum of all pie percentages?	100 % (or 360° for angles).
Pie chart angle	How to compute the angle of a sector?	((\text{part}/\text{whole}) \times 360^\circ).
Conversion	Convert 25 % of a pie to degrees.	(25% \times 360^\circ = 90^\circ).
Comparison	Which chart better shows that “Theft” is the highest?	Bar chart (height comparison).
Application	When would you prefer a pie chart over a bar chart?	When you need to show proportions of a whole.

Tip for Exam

Always check that pie chart percentages add up to 100 %.
In bar charts, always read the axis, not just the bar length.
For quick calculations, use the “percentage‑to‑degree” shortcut: 1 % = 3.6°.

**Good luck with your preparation!