Bar & pie charts: Quantitative Aptitude Notes for Haryana Patwari / Lekhpal

Bar & Pie Charts

Quantitative Aptitude – Haryana Patwari / Lekhpal Examination

1. Simple Explanation

Chart Type	What It Shows	When to Use
Bar Chart	Comparison of discrete categories (e.g., sales of 5 products)	When you need to compare whole numbers or percentages across categories
Pie Chart	Parts of a whole – each slice is a percentage of 100%	When you want to show how a total is divided among categories

Bars are vertical (or horizontal) rectangles.
Slices in a pie chart are sectors of a circle.
Both charts are visual tools that make it easy to spot the largest or smallest category, the proportion of each part, and the overall trend.

2. Key Points & Important Formulas

Concept	Key Points	Formula (if any)
Reading a Bar Chart	• Each bar’s height (or length) is proportional to the value. • The y‑axis (or x‑axis) gives the scale. • Look at the labels on the axis and the numbers at the top of each bar.	Value of a bar = (Bar height ÷ Scale unit) × Scale multiplier
Reading a Pie Chart	• The whole circle = 100%. • Each slice’s angle (in degrees) is proportional to its percentage. • The sum of all slice percentages = 100%.	Percentage of a slice = (Angle of slice ÷ 360°) × 100%
Finding Missing Percentage in a Pie Chart	• Sum of given percentages < 100%. • Missing part = 100% – (sum of given percentages).	Missing % = 100% – Σ given %
Finding Missing Value in a Bar Chart	• If you know the total and the percentage of a bar, you can compute its value. • If you know the percentage of a bar and the total value, multiply.	Bar value = (Percentage ÷ 100%) × Total
Comparing Two Bars	• Compare the heights directly or by converting to percentages. • “Higher bar” → larger value.	–
Converting Between Bar Chart & Pie Chart	• If a bar chart’s values are known, compute each value’s share of the total to draw a pie chart. • If a pie chart’s percentages are known, multiply by the total to get the actual values.	–
Common Mistakes	• Misreading the scale (e.g., 10 units = 1000). • Assuming all bars are same width; some charts use variable widths. • Forgetting that a pie chart’s slice angles sum to 360°.	–

3. Worked Example

Problem

A bar chart shows the number of farmers who own 5 types of livestock in a village:

Livestock	Number of Farmers
Cattle	120
Pigs	80
Goats	160
Sheep	100
Chickens	200

Which type has the highest number of farmers?
What percentage of farmers own chickens?
Convert the bar chart data into a pie chart and state the angle (in degrees) of the slice for goats.

Solution

1. Highest Number

Compare the numbers: 120, 80, 160, 100, 200.
Chickens has the highest number (200 farmers).

2. Percentage of Farmers with Chickens

Total farmers = 120 + 80 + 160 + 100 + 200 = 660.
Percentage for chickens = (200 ÷ 660) × 100% ≈ 30.30%.

3. Pie Chart Slice for Goats

Goats count = 160.
Percentage for goats = (160 ÷ 660) × 100% ≈ 24.24%.
Angle of goat slice = (24.24% ÷ 100%) × 360° ≈ 87.27°.

Summary of Results

Livestock	Value	% of Total	Slice Angle (°)
Cattle	120	18.18%	65.45°
Pigs	80	12.12%	43.64°
Goats	160	24.24%	87.27°
Sheep	100	15.15%	54.55°
Chickens	200	30.30%	109.09°

4. Quick Revision Summary

Bar chart – uses bar heights to represent discrete values; read the scale for exact numbers.
Pie chart – each slice’s angle represents its share of 100%; sum of all angles = 360°.
Missing part:
- Pie chart: Missing % = 100% – Σ given %.
- Bar chart: If total is known, missing bar value = Total × (Missing % ÷ 100%).
Comparisons: Highest bar ↔ largest value; Largest slice ↔ largest percentage.
Conversions:
- Bar → Pie: Percentage = (Bar value ÷ Total) × 100%.
- Pie → Bar: Bar value = (Percentage ÷ 100%) × Total.
Common pitfalls: Wrong scale, mixing up percentages and raw numbers, ignoring that pie angles sum to 360°.

Use these steps to decode any bar or pie chart quickly during your exam!