📚 Study Notes – “Average”
For the Arunachal Pradesh Police Constable Exam – Quantitative Aptitude
1. What is an “Average”?
-
Simple definition
The average is what each item would get if the total is shared equally. -
Everyday analogy
Imagine you have 5 mangoes and you want to give them to 5 friends.
Each friend gets 1 mango.
The number each friend receives (1) is the average.
2. How to Find the Average (Mean)
| Step | What to do | Example |
|---|---|---|
| 1️⃣ | Add all the numbers. | 4 + 8 + 12 + 16 = 40 |
| 2️⃣ | Count how many numbers there are. | 4 numbers |
| 3️⃣ | Divide the sum by the count. | 40 ÷ 4 = 10 |
| ✔️ | Result = Average | 10 |
Formula
[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of items}} ]
3. Tiny Example
| Marks in 4 subjects | 78 | 82 | 90 | 85 |
|---|---|---|---|---|
| Sum | 78 + 82 + 90 + 85 = 335 | |||
| Count | 4 | |||
| Average | 335 ÷ 4 = 83.75 |
So the student’s average mark is 83.75.
4. Quick Tips for the Exam
- Always check the units – if numbers are in thousands, keep them as such.
- Round only if the question asks – otherwise give the exact decimal.
- Double‑check your addition – one small mistake ruins the average.
- Practice with real numbers – try calculating averages for daily expenses, distances, etc.
5. Mini Practice Problems
| Problem | Your Answer |
|---|---|
| 1. Five numbers: 12, 15, 18, 21, 24. Find the average. | |
| 2. The monthly sales (in ₹k) for a shop in Jan–Mar are 22, 27, 19. What’s the average monthly sale? | |
| 3. A police constable’s daily steps over 4 days: 3000, 3500, 3200, 3100. Calculate the average steps per day. |
Answers
- 18.0
- 22.67 (₹k)
- 3175 steps
6. Summary
- Average = Total ÷ Count
- Add all numbers → Count them → Divide
- Keep calculations simple, double‑check, and practice!
Good luck on your exam! 🚀