📊 Average – SSC Cheat Sheet
📌 What is Average?
Average (or Arithmetic Mean) is a central value of a set of numbers.
It is calculated by dividing the total sum of values by the number of values.
✅ Formula:
Average = (Sum of quantities) ÷ (Number of quantities)
🧠 Important Formulas & Shortcuts
1. Average of First n Natural Numbers:
= (n + 1) / 2
2. Average of First n Even Numbers:
= (n + 1)
3. Average of First n Odd Numbers:
= n
4. Adding/Removing Items:
- If a number x is added or removed, new average changes by: Change = (x – Average) / n
⚡ Smart Tricks
➤ When all quantities increase/decrease by the same value:
👉 Average increases/decreases by that same value.
➤ Assume values when no actual data is given:
Use "Let average = x" and build the equation around it.
➤ Average of consecutive numbers:
Average = middle term
For odd count → Middle term
For even count → Average of middle two terms
🧠 Mental Shortcuts
Break big numbers:
Eg: Average of 98, 99, 101
→ Think of them as close to 100
→ Differences: –2, –1, +1 ⇒ Average = 100 – 2/3 ≈ 99.33Use base average (assumed number)
→ Adjust deviations from that base
📘 SSC PYQs – With Tricks
🔹 SSC CGL 2022
Q: Average of 5 numbers is 42. One more number is added and average becomes 44. Find the new number.
Sol:
Total of 5 numbers = 5×42 = 210
New total = 6×44 = 264
New number = 264 – 210 = 54 ✅
🔹 SSC CHSL 2021
Q: Find average of first 10 odd natural numbers.
Sol:
Formula: Average = n
n = 10 ⇒ Answer = 10 ✅
🔹 SSC MTS 2020
Q: Average of 4 numbers is 65. The fifth number is 75. Find new average.
Sol:
Total = 65×4 = 260
New total = 260 + 75 = 335
Average = 335 ÷ 5 = 67 ✅
🔹 SSC GD 2019
Q: Average of 8 numbers is 25. If one number is wrongly taken as 20 instead of 30, find correct average.
Sol:
Wrong total = 25×8 = 200
Correct total = 200 + (30 – 20) = 210
Correct average = 210 ÷ 8 = 26.25 ✅
📊 Practice Examples
1. Find average of 21, 25, 29, 33, 37
👉 Total = 145 ⇒ Average = 145 ÷ 5 = 29
2. Average of 10 numbers is 45. If one number is 15 more than average, what is it?
👉 45 + 15 = 60
3. Average of 6 numbers is 72. One more number added becomes 70. Find new number.
👉 72×6 = 432 ⇒ 70×7 = 490
⇒ New number = 490 – 432 = 58
📌 Flash Summary
🔢 Average = Sum ÷ Count ➕ If equal changes made → Avg shifts equally 🧠 Assume base to simplify 📊 Know avg formulas: odd, even, natural numbers
🔁 Rapid Revision Table
| Type | Formula/Result |
|---|---|
| Avg of n natural numbers | (n + 1)/2 |
| Avg of n even numbers | (n + 1) |
| Avg of n odd numbers | n |
| Avg change (added/removed item) | (x – Avg) / n |
| Avg of consecutive numbers | Middle term |
🎯 Tips for SSC Aspirants
- Practice SSC PYQs from last 5 years
- Time yourself – average questions test speed + logic
- Don't memorize numbers — understand patterns
- Revise formulas weekly for retention
📈 Practice Daily!
✔️ Solve 15–20 average-based questions every day
✔️ Revise mental math tricks and approximation daily
✔️ Target topics: Time & Work, Profit & Loss, and Simplification after Average
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Let’s crack SSC, together. 💪