📊 Quantitative Aptitude – Average (Mean)
1. What is an Average?
- Think of a bucket that holds all the numbers.
- The average is the amount each number would have if the bucket were split evenly.
- Everyday example:
You and 4 friends have 5, 7, 9, 6, and 8 candies.
Total candies = 5 + 7 + 9 + 6 + 8 = 35.
If you share them equally, each person gets 35 ÷ 5 = 7 candies.
7 is the average.
2. How to Find the Mean (Average)
- Add all the numbers together.
- Count how many numbers you added.
- Divide the total by that count.
Formula:
[
\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}}
]
3. Tiny Example
| Score | 5 | 7 | 9 | 6 | 8 |
|---|---|---|---|---|---|
| Sum | 35 | ||||
| Count | 5 | ||||
| Average | 7 |
- Total = 35
- Count = 5
- Average = 35 ÷ 5 = 7
4. Common Mistakes & How to Avoid Them
| Mistake | What Went Wrong | Quick Fix |
|---|---|---|
| Forgetting to count | Sometimes you think there are 4 numbers, not 5. | Double‑check the list. |
| Wrong addition | Adding 5 + 7 + 9 + 6 + 8 incorrectly. | Write each step; use a calculator if needed. |
| Dividing by the wrong number | Using 4 instead of 5. | Confirm the count again. |
| Mixing up “average” with “median.” | Thinking “average” means the middle value. | Remember average is sum ÷ count. |
5. Quick Tips
-
Shortcuts
- If numbers are close together, estimate the average by rounding them first, then refine.
- For a quick mental check, add the smallest and largest numbers; they often give a good sense of the average.
-
Check Reasonableness
- The average must lie between the smallest and largest numbers.
- If it falls outside that range, re‑calculate.
6. Practice Problems
| # | Numbers | Find the average |
|---|---|---|
| 1 | 4, 6, 8, 10 | |
| 2 | 12, 15, 18, 21, 24 | |
| 3 | 3, 3, 3, 3, 3 | |
| 4 | 7, 14, 21, 28 | |
| 5 | 2, 5, 9, 12, 15, 18 |
7. Answers
| # | Numbers | Average |
|---|---|---|
| 1 | 4, 6, 8, 10 | 7 |
| 2 | 12, 15, 18, 21, 24 | 18 |
| 3 | 3, 3, 3, 3, 3 | 3 |
| 4 | 7, 14, 21, 28 | 17.5 |
| 5 | 2, 5, 9, 12, 15, 18 | 10.5 |
8. Summary
- Average = total of numbers ÷ how many numbers.
- Always add first, then count, then divide.
- Check that the result is between the smallest and largest numbers.
- Practice with real‑life sets of numbers to get comfortable.
You’re now ready to tackle any average problem in JNU Entrance Quantitative Aptitude! 🚀