Bar Charts, Line Graphs & Percentage Change

🎯 Learning Objective

Read bar and line graphs and correctly compute percentage increase or decrease using the OLD value as the base.

💡 Concept

• Bar graph → height of each bar is the value; Line graph → each point's height is the value, the line just shows the trend
• Percentage change = (Change ÷ Original value) × 100
• The base (denominator) is ALWAYS the older / previous value, never the new one
• Increase → answer is positive; Decrease (drop) → use the same formula on the fall
• Total and average across years work just like in tables

🧮 Key Formulas

Percentage change = (New − Old) ÷ Old × 100

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Average = Total ÷ Number of years

✏️ Easy Example

Q. A bar graph shows candidates (in thousands) who appeared for an exam: 2019 = 40, 2020 = 50, 2021 = 45, 2022 = 60, 2023 = 75. Find the percentage increase from 2019 to 2020.

1. Change = 50 − 40 = 10
2. Percentage = (10 ÷ 40) × 100

Answer: 25%

🇮🇳 Real-Life Example

News channels love the line — 'petrol prices up 25% this year!'. They just took this year minus last year, divided by last year. Now you can check whether the headline is honest.

📝 Exam-Level Example

Q. Using the same bar graph (2019 = 40, 2020 = 50, 2021 = 45, 2022 = 60, 2023 = 75 thousand), find the total and average number of candidates over the 5 years.

1. Total = 40 + 50 + 45 + 60 + 75 = 270 thousand
2. Average = 270 ÷ 5

Answer: Total 270 thousand, Average 54 thousand

📝 Exam-Level Example

Q. A line graph shows quarterly sales (₹ lakh): Q1 = 50, Q2 = 60, Q3 = 45, Q4 = 54. Find the percentage drop from Q2 to Q3.

1. Drop = 60 − 45 = 15
2. Base = old value = 60
3. Percentage drop = (15 ÷ 60) × 100

Answer: 25%

📝 Exam-Level Example

Q. From the same bar graph, what is the percentage increase from 2021 (45) to 2022 (60)?

1. Change = 60 − 45 = 15
2. Percentage = (15 ÷ 45) × 100 = 33.33%

Answer: 33.33% (an increase of one-third)

🪄 Memory Trick

Divide the change by the SMALLER (older) number to increase, and it's a jump; a fall of x from base B is always x/B. Fix 'base = previous value' in your head.

⚠️ Common Mistakes

• ❌ Using the new value as the base instead of the old one
• ❌ Confusing percentage increase with actual increase
• ❌ Reading a line graph's slope as the value instead of the point's height

🏆 Exam Tips

• ✅ Base = previous value — write it before dividing
• ✅ A 33.33% rise means '×4/3', a 25% rise means '×5/4' — learn these shortcuts

📌 Summary

• Bar/line height = the value
• Percentage change = change ÷ OLD value × 100
• Base is always the previous value
• Total and average work exactly like tables