📚 Himachal Pradesh PSC – Quantitative Aptitude
Topic: Average
1️⃣ Simple Explanation
The average (also called the mean) is a measure of central tendency that represents the “typical” value in a set of numbers.
Average = (Sum of all values) ÷ (Number of values)
2️⃣ Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Definition | Average = Total ÷ Count |
| 2 | Integer vs. Fraction | The result can be an integer or a fraction; round only if the question asks. |
| 3 | Weighted Average | Average = (Σ weight × value) ÷ Σ weight – Used when items have different importance. |
| 4 | Changing the Average | Adding a new value changes the numerator and denominator. |
| 5 | Average of Averages | If you have groups, you can find the overall average by taking a weighted average of the group averages. |
| 6 | Common Pitfalls | • Mixing up sum and count. • Forgetting to include all values. • Using the wrong formula for weighted average. |
| 7 | Quick Checks | • If the average is an integer, the sum must be divisible by the count. • If adding a value > current average, the new average increases; if < current average, it decreases. |
3️⃣ Worked Example
Question (Typical PSC Type)
A class of 30 students has an average score of 68 in Mathematics.
Six more students join the class and score 70 each.
What is the new average score of the class?
Step‑by‑Step Solution
| Step | Action | Calculation | Result |
|---|---|---|---|
| 1 | Find original total score | Average × Number = 68 × 30 |
2040 |
| 2 | New total after 6 students | 2040 + (70 × 6) |
2040 + 420 = 2460 |
| 3 | New number of students | 30 + 6 = 36 |
|
| 4 | New average | 2460 ÷ 36 |
68.333… ≈ 68.33 |
Answer: The new average is ≈ 68.33.
Quick Check: 70 > 68 → average should increase → 68.33 is indeed higher.
4️⃣ Quick Revision Summary
| Topic | Formula | Example Use |
|---|---|---|
| Simple Average | Avg = Σx ÷ n |
Find average of 4 exam scores. |
| Weighted Average | Avg = (w₁x₁ + w₂x₂ + …) ÷ (w₁ + w₂ + …) |
Compute average cost of items with different quantities. |
| Effect of Adding a Value | If new value > current average → average ↑; else → average ↓ | Decide whether to accept a new applicant based on average test score. |
| Average of Averages | Overall Avg = (n₁Avg₁ + n₂Avg₂ + …) ÷ (n₁ + n₂ + …) |
Combine averages from two classes. |
| Quick Check | Sum must be divisible by count for integer average | Verify results in exam solutions. |
Tip for PSC:
- Always verify that the sum uses all numbers mentioned.
- If the problem mentions "average of averages", use the weighted‑average method.
- Watch out for phrasing like "average score of boys and girls separately", which may require two separate calculations before combining.
Good luck with your preparation! 🚀