MPESB Group · Bite-size lessons
Average
About 6 min · Mathematics · English
Time worked out from the lesson's 441 words at 150 words a minute, plus a minute for each question.
Average is one of the most fundamental concepts in quantitative aptitude. Questions on average test your ability to quickly calculate mean values, handle additions or removals from groups, and work with weighted data sets. This topic forms the foundation for understanding more complex concepts like statistics, data interpretation, and mixture problems.
Key ideas
- Arithmetic Mean is the sum of all observations divided by the total number of observations. It represents the central value of a data set.
- Weighted Average assigns different weights (importance) to different values. Use this when items contribute unequally to the total.
- Average of a series: For consecutive numbers, the average equals the middle term (or the mean of the two middle terms when the count is even). For an AP, average = (first term + last term) ÷ 2.
- Effect of adding/removing items: When a new item is added, the change in average depends on how far the new item is from the old average.
- Replacement concept: When one item replaces another, the change in sum equals (new item − old item), and this affects the average proportionally.
Watch out for
- Using simple average for speed problems → For equal distances traveled at different speeds, always use the harmonic mean formula: 2×S₁×S₂÷(S₁+S₂). Simple average only works when equal time is spent at each speed.
- Forgetting to update the count → When a person joins or leaves, students often calculate the new sum but divide by the old count. Always track whether the number of items has changed.
- Confusing weighted average conditions → Use weighted average only when different items have different importance or quantities. If all items are equally weighted, simple average works.
Quick reference
- Average = Sum ÷ Count; Sum = Average × Count
- First n natural numbers: Average = (n+1)/2
- Average speed for equal distances = 2ab/(a+b)
- New member's value = (New avg × New count) − (Old avg × Old count)
- When one value changes by x, average changes by x/n
Check yourself: 3 questions
1. The average age of 5 students in a class is 14 years. If the age of the teacher is also included, the average age increases by 2 years. What is the age of the teacher?
2. A cricketer has scored an average of 42 runs in 10 innings. How many runs must he score in his 11th innings to raise his average by 3 runs?
3. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
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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