UPSSSC PET · Bite-size lessons
Average
About 6 min · Elementary Arithmetic · English
Time worked out from the lesson's 399 words at 150 words a minute, plus a minute for each question.
It tests your ability to find central tendencies in numerical data and solve word problems involving groups, ages, weights, marks, speeds, and incomes. Mastery of average is essential not just for direct questions but also for time-speed-distance problems, age-based puzzles, and data interpretation sections.
Key ideas
- Average (Arithmetic Mean) is the sum of all observations divided by the number of observations: Average = Total Sum ÷ Number of Items. It represents the central value that would result if all quantities were equal.
- Total Sum Relationship: If you know the average and count, you can find the total: Total = Average × Number of Items. This reverse calculation is crucial for multi-step problems.
- Effect of Adding/Removing Items: When a new member joins or leaves, the average changes. The change depends on whether the new value is above or below the current average. Calculate new total, then divide by new count.
- Replacement Effect: When one item replaces another, the change in total equals (new value – old value). The average change equals this difference divided by the total number of items.
- Weighted Average: When different groups have different counts, you cannot simply average the averages. You must find total sum of all groups combined, then divide by total count: Weighted Average = (Sum₁ + Sum₂ + ... + Sumₙ) ÷ (Count₁ + Count₂ + ... + Countₙ).
Quick reference
- Core Formula: Average = Sum ÷ Count; conversely Sum = Average × Count
- Consecutive integers: Average = (First + Last) ÷ 2 = Middle term
- n natural numbers: Average = (n + 1) ÷ 2; n odd numbers: Average = n
- Weighted average requires totals: Never average averages of unequal groups
- New member impact: New Avg = (Old Total + New Value) ÷ (Count + 1)
Check yourself: 3 questions
1. The average weight of 5 boys is 52 kg. If one boy weighing 56 kg leaves the group, what is the average weight of the remaining 4 boys?
2. A student scores 65, 72, 58, 80 and x marks in five subjects. If his average score is 70 marks, what is the value of x?
3. The average age of a group of 20 students is 18 years. When 5 new students with an average age of 16 years join the group, what is the new average age of all 25 students?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 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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