Average Questions for SSC CGL

Basic Concept of Average

Average (or Arithmetic Mean) is the equal share each item would get if the total were distributed evenly. Think of it as levelling a bumpy field — every bump and dip becomes flat at the average height. The formula is simple: sum all values, divide by count. The key insight is that Average x Count = Total Sum. This relationship is what drives almost every average problem.

• Average = Sum of all items / Number of items
• Sum = Average x Number of items — memorise this, it unlocks most problems
• If all values are equal, average equals that value
• Average always lies between the smallest and largest value in the group
• Adding or subtracting the same number from all items shifts the average by that number

Effect of Adding or Removing a Member

When a new person joins or leaves a group, the average changes. The trick is to work with total sums. New Sum = Old Sum plus or minus the new value. Then divide by the new count. SSC CGL loves questions like: a group's average age increases by 2 when a new person joins — find the new person's age.

• New person's value = New Average x New Count - Old Average x Old Count
• If average increases after adding a member, new member's value is above old average
• If average decreases after adding a member, new member's value is below old average
• Change in sum = Change in average x new count
• For removal: Removed value = Old Average x Old Count - New Average x New Count

Replacement Problems

One of the most frequently tested patterns in SSC CGL. One person is replaced by another and the average changes. The logic: the new person compensates for the change in average across all members. If average rises by 2 after replacing one person in a group of 10, the new person is 20 more than the old person.

• Change in total sum = Change in average x total count
• New person's value = Old person's value + (Change in avg x total count)
• If average increases, new person is heavier/older/higher
• If average decreases, new person is lighter/younger/lower
• Watch sign: increase means new person added more to the sum

Average of Consecutive Numbers

For consecutive integers, evenly spaced numbers, or APs (Arithmetic Progressions), the average equals the middle term (or average of first and last term). This is a huge time-saver in SSC CGL. No need to add all numbers.

• Average of 1 to n = (n+1)/2
• Average of first n odd numbers = n
• Average of first n even numbers = n+1
• Average of an AP = (First term + Last term) / 2
• For consecutive integers from a to b: Average = (a+b)/2

Weighted Average

When two groups with different averages are combined, you cannot simply average the two averages. You must use weighted average. Think of it as a tug of war — the group with more members pulls the combined average closer to its side.

• Weighted Avg = (n1 x A1 + n2 x A2) / (n1 + n2)
• Combined average is always between the two individual averages
• The larger group pulls the average closer to its own average
• Used heavily in DI sets and mixture problems
• Alligation rule is a shortcut — ratio of members = ratio of distances from combined average

• Forgetting to update the count when a person is added or removed — always adjust n first
• Averaging two averages directly without weighting by group size — classic trap in combined group questions
• Sign error in replacement: if average increases, new value is OLD + (change x count), not OLD - (change x count)
• Confusing 'average of first n odd numbers = n' with 'average of first n even numbers = n' — they differ by 1
• In age problems, not accounting for time passage — if average age of a group increases by 1 each year, that is the expected natural increase, so any extra change signals a replacement or addition

• SAN triangle: Sum = Average x Number. Cover any one corner to get the formula. Like Speed-Distance-Time triangle.
• REPLACEMENT shortcut: think of it as the new person COMPENSATING everyone. Extra per person x number of persons = total extra that new person brings.
• For consecutive numbers: Middle is the Average. No calculation needed — just find the middle term.
• Weighted average tug of war: heavier team (more members) wins — the combined average leans toward the bigger group.

• SSC CGL typically asks 2-3 average questions per tier — usually one replacement problem, one age-based problem, and one consecutive numbers or weighted average problem.
• Replacement and addition/removal questions are 80 percent of PYQ patterns — master the Sum = Avg x Count formula and you solve them in under 30 seconds.
• In Tier 1 time pressure, use the shortcut for consecutive integers always — never add them manually.
• Age problems often disguise themselves as average problems. Translate every sentence into a Sum equation before solving.
• In Data Interpretation sets, average calculation is the most common operation. Practice reading table values quickly and applying Sum = Avg x n to find missing entries.