Average
About 6 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 355 words at 150 words a minute, plus a minute for each question.
It tests your ability to find the central value of a group of numbers and apply this concept to real-world scenarios like age problems, marks, income, expenses, and weights.
Key ideas
- Average (Arithmetic Mean) is the sum of all observations divided by the number of observations. It represents the central or typical value of a dataset.
- Sum = Average × Number of observations. This reverse formula is the most powerful tool for solving average problems quickly. Memorize it.
- When a new member joins or leaves a group, the total sum changes. Calculate the new sum, then find the new average by dividing by the new count.
- Weighted Average applies when different groups contribute unequally to the total. You cannot simply average the averages—you must account for the size of each group.
- In age problems, if n years pass, every person's age increases by n years, so the average age also increases by n years. If k people join or leave, recalculate the sum and divide by the new count.
Quick reference
- Average = Sum / Count; Sum = Average × Count (use this reverse formula constantly)
- Weighted average requires summing (group size × group average) for all groups, then dividing by total count
- When time passes equally for everyone, average age increases by exactly that time period
- When one value is added: new sum = old sum + new value; new count = old count + 1
- Change in total sum = Change in average × Number of observations
Check yourself: 3 questions
1. The average of five numbers is 42. If one number is excluded, the average of the remaining four numbers becomes 38. What is the excluded number?
2. The average weight of 40 students in a class is 52 kg. If the teacher's weight is also included, the average weight increases by 1 kg. What is the weight of the teacher?
3. The average age of a father and his son is 30 years. The average age of the father, mother and son is 32 years. What is the age of the mother?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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