Average

Simple, combined, and weighted averages — including replacement and inclusion/exclusion problems.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Average = Sum of observations ÷ Number of observations

Situation	Formula
Combined average of two groups	(n₁×A₁ + n₂×A₂) / (n₁+n₂)
Average of first n natural numbers	(n+1)/2
Average of first n even numbers	n+1
Average of first n odd numbers	n

Work with totals (Sum = Average × Count) rather than averages directly — converts the problem to simple addition/subtraction
If a new member is included: New Sum = Old Sum + New Member's Value
If a member is replaced: Change in total = (New Average − Old Average) × Total Count

💡 Example: Average age of 30 students is 12. Including the teacher, average becomes 13. Teacher's age = (31×13) − (30×12) = 403 − 360 = 43 years.

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