📚 Madhya Pradesh PSC – Quantitative Aptitude
Topic: Average (Arithmetic Mean)
1️⃣ What is an Average?
- Average tells you the “typical” value in a set of numbers.
- Think of it like the middle point that balances all the numbers.
Analogy:
Imagine you have 5 friends who each bought a different number of candies.
To find the average candies per friend, you add all candies together and then split them equally among the 5 friends.
2️⃣ How to Calculate the Average
Step‑by‑step (no fancy terms)
- Add all the numbers together.
- Count how many numbers there are.
- Divide the total sum by the count.
Quick Formula (in plain text)
[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of items}} ]
3️⃣ Tiny Example
| Numbers | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| Sum | 30 | ||||
| Count | 5 | ||||
| Average | 6 |
Explanation:
- Add: 2 + 4 + 6 + 8 + 10 = 30
- Count: 5 numbers
- Divide: 30 ÷ 5 = 6
So the average number of candies per friend is 6.
4️⃣ Quick Practice Problems
| Problem | Your Answer | Correct Answer |
|---|---|---|
| 1. Average of 3, 9, 12 | 8 | |
| 2. Average of 5, 7, 8, 10 | 7.5 | |
| 3. Average of 4, 4, 4, 4, 4 | 4 |
How to solve
- Add the numbers.
- Count them.
- Divide.
Tip: If the sum is not divisible evenly, you’ll get a decimal – just keep the fraction or round if the question asks for a whole number.
5️⃣ Common Mistakes to Avoid
| Mistake | Why it happens | Fix |
|---|---|---|
| Dividing by the wrong number | Forgetting to count all items | Write down the count before dividing |
| Forgetting to add all numbers | Skipping a value | List every number in a row |
| Rounding too early | Rounding each addition step | Add first, then round (if needed) |
6️⃣ Everyday Uses of Average
| Situation | What the average tells you |
|---|---|
| Test scores | Typical performance of a student group |
| Daily temperature | How hot or cold it usually feels |
| Speed of a car | Typical speed over a trip |
| Salary of employees | Normal earning level in a company |
7️⃣ Quick Reference Cheat‑Sheet
| Step | Action | Example |
|---|---|---|
| 1 | Add numbers | 2 + 4 + 6 = 12 |
| 2 | Count numbers | 3 items |
| 3 | Divide sum by count | 12 ÷ 3 = 4 |
8️⃣ Final Tip
- Practice with real data: Try finding the average of your own daily steps, the number of books read in a month, or the price of items you bought.
- The more you do it, the faster you’ll get!
Happy learning! 🚀