Bar & pie charts

📊 Bar & Pie Charts – Quantitative Aptitude

(For Jammu & Kashmir Patwari / Lekhpal Exam)

Why Learn This?
Bar and pie charts are the most common ways to present data in exams.
They test your ability to read, interpret, and perform simple calculations with percentages, ratios, and angles.

1. Simple Explanation

2. Key Points to Remember

Bar Charts

1. Axis

   • X‑axis (horizontal) – categories
   • Y‑axis (vertical) – numeric scale (often in units, thousands, etc.)

2. Reading Values

   • Read the bar’s height from the Y‑axis.
   • If bars are in units of 100, a bar that reaches 8 on the axis actually means 800.

3. Comparisons

   • “Bar A is higher than Bar B” → A’s value > B’s value.
   • “Bar B is twice Bar A” → B’s height = 2 × A’s height.

4. Missing Data

   • Sometimes one bar’s height is missing.
   • Use given relationships to calculate it.

5. Common Mistakes

   • Misreading the scale (e.g., 100 = 1000).
   • Assuming equal spacing between bars equals equal values.

Pie Charts

1. Whole – 360° represents 100%.
2. Angle ↔ Percentage
   • Angle (°) = (Percentage ÷ 100) × 360
   • Percentage = (Angle ÷ 360) × 100
3. Area – proportionally same as angle (for a regular pie).
4. Missing Slice – Sum of all percentages = 100%.
5. Common Mistakes
   • Using 30° as 30% instead of 8.33%.
   • Forgetting that 360° corresponds to 100%.

3. Worked Example

Problem (Bar Chart)

Given: Revenue in 2021 is 25% less than 2020.
Question: Draw the bar chart and find the revenue for 2021.

Solution

1. Find 2021 revenue

   • 25 % less than 180 → (180 \times (1 - 0.25) = 180 \times 0.75 = 135) lakhs.

2. Bar chart – (illustrated in the description, but here is a simple ASCII representation)

₹220 |                          █
₹200 |                          █
₹180 |            █             █
₹160 |            █             █
₹140 |            █             █
₹120 | █          █             █
₹100 | █          █             █
      --------------------------------
        18  19  20  21  22

The bars’ heights correspond to the revenues above.

Problem (Pie Chart)

A company’s market share:

• Company A – 30%
• Company B – 25%
• Company C – 15%
• Company D – remaining share

Questions

1. What is the angle of Company D’s slice?
2. If the pie chart is drawn on a paper where 1° = 1 cm, how long is the arc of Company D’s slice?

Solution

1. Find Company D’s percentage

   • (100 - (30 + 25 + 15) = 100 - 70 = 30%)

2. Angle for Company D

   • (\theta = \frac{30}{100} \times 360 = 108^\circ)

3. Arc length

   • Arc length ( = \theta \times (\text{radius})).
     – If radius = 1 cm (since 1° = 1 cm, radius = 1 cm)
     – (L = 108^\circ \times \frac{\pi}{180} \text{ rad} \times 1 \text{ cm} \approx 1.884 \text{ cm})

4. Quick Revision Summary

5. Practice Questions (Try Without Looking at the