Average
About 6 min · Quantitative Ability · English
Time worked out from the lesson's 396 words at 150 words a minute, plus a minute for each question.
Average is a core topic in the Quantitative Ability section of HSSC CET. It appears both as direct calculation questions and as a component within other topics like Data Interpretation, Time and Distance, and Profit-Loss problems.
Key ideas
- Simple Average = Sum of all observations ÷ Number of observations. All items carry equal importance.
- Weighted Average applies when different items have different weights or frequencies. Each value is multiplied by its weight before summing.
- The Sum Principle: Average × Number of items = Total Sum. This relationship is the foundation of almost every average problem.
- Effect of adding/removing an item: When a new value is added, the change in average depends on how far the new value is from the old average.
- Average of consecutive numbers: For any arithmetic progression, the average equals the middle term (or average of two middle terms if count is even).
Watch out for
- Mistake: Adding averages directly when combining groups. Fix: Always calculate total sums first, then divide by total count. Averages cannot be added directly unless group sizes are equal.
- Mistake: Forgetting that average changes when the group size changes. Fix: If a person joins or leaves, recalculate using new count. Average = New Sum ÷ New Count.
- Mistake: Confusing "average of first n even numbers" with "average of even numbers from 1 to n." Fix: First 5 even numbers are 2,4,6,8,10 (avg = 6). Even numbers from 1 to 5 are 2,4 (avg = 3). Read carefully.
Quick reference
- Average = Sum ÷ Count — the only formula you truly need.
- To find sum: Multiply average by count.
- Consecutive numbers a to b: Average = (a + b) ÷ 2.
- First n natural numbers: Average = (n + 1) ÷ 2.
- When one value changes by x: Average changes by x ÷ n.
Check yourself: 3 questions
1. The average of five numbers is 48. If one number is excluded, the average of the remaining four numbers becomes 45. What is the excluded number?
2. A batsman has scored an average of 52 runs in 10 innings. How many runs must he score in his 11th innings to increase his average to 54?
3. The average weight of 30 students in a class is 45 kg. If the teacher's weight is included, the average weight increases by 1 kg. What is the weight of the teacher?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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