Average — The Balancing Point

🎯 Learning Objective

Compute averages and use total = average × count as the master tool.

💡 Concept

• Average = Sum of items ÷ Number of items
• The reverse is more useful: SUM = AVERAGE × COUNT
• Average always lies between the smallest and largest value
• Adding a value equal to the average keeps the average unchanged

🧮 Key Formulas

Average = Sum ÷ Count

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Sum = Average × Count

✏️ Easy Example

Q. The average of 5 numbers is 20. What is their sum?

1. Sum = Average × Count
2. = 20 × 5

Answer: 100

🇮🇳 Real-Life Example

Your cricket batting average: total runs ÷ innings. Virat Kohli's average works exactly like your exam questions.

📝 Exam-Level Example

Q. Average of 10 numbers is 15. If one number 25 is removed, find the new average.

1. Total = 10 × 15 = 150
2. New total = 150 − 25 = 125
3. New average = 125 ÷ 9 ≈ 13.89

Answer: 13.89 (125/9)

🪄 Memory Trick

Never juggle averages — convert to totals immediately, operate, convert back.

⚠️ Common Mistakes

• ❌ Averaging two averages directly without weighting
• ❌ Forgetting count changes when items are added/removed

🏆 Exam Tips

• ✅ Write Sum = A × N as your first line for every question
• ✅ Answer must lie between min and max — sanity check

📌 Summary

• Sum = Average × Count is the key
• Work with totals, not averages
• Average lies between extremes