Quantitative Aptitude
Average
Average
Average (Arithmetic Mean) is the sum of all values divided by the count. Most exam problems twist this by adding/removing members, replacing a wrong entry, or combining two groups.
Key Idea
Work backwards from Average: Sum = Average × Count. This single formula solves 80% of average problems.
Core Formulas
Average
Average = Sum / Count → Sum = Average × Count
First step in any average problem — compute the total sum from given average and count.
Weighted Average
Combined Avg = (n₁×a₁ + n₂×a₂) / (n₁ + n₂)
When two groups of different sizes are merged and you need the overall average.
Effect of Adding a New Term
New term = New Avg × (n+1) − Old Avg × n
When the average changes after one more element is included.
Effect of Replacing a Term
Change in average = (New value − Old value) / n
When one member leaves and another joins — find how much the average shifts.
Average of Consecutive Integers
Avg = (First + Last) / 2 = middle term
For any evenly-spaced sequence; the average equals the middle value.
Relevant Exams
Average questions appear in virtually every banking and SSC exam — replacement and weighted-average variants are the most tested sub-types.