Average Questions for AGNIVEER ARMY

What is Average

Average means the equal share everyone would get if you distributed the total equally. Think of it like this: 5 friends pool their money and split it equally — that equal share is the average. In maths terms, average is the sum of all values divided by the count of values.

• Average = Sum of all items / Number of items
• Sum = Average x Number of items (very useful shortcut)
• Number of items = Sum / Average
• Average always lies between the smallest and largest value in the group
• If all values are equal, average equals that same value

Average of Consecutive Numbers

For consecutive numbers or an evenly spaced series (like consecutive even, consecutive odd), the average is simply the middle value, or the average of the first and last number. This is a big time-saver in the exam.

• Average of 1 to n = (n+1)/2
• Average of first n even numbers = n+1
• Average of first n odd numbers = n
• Average of any arithmetic series = (First term + Last term) / 2
• For symmetric set like {10,20,30,40,50}: average = middle term = 30

New Member Added or Removed — Change in Average

A very common question type: a person joins or leaves a group and the average changes. The trick is to think in terms of total sum. When someone joins, the new total must match the new average. Use the formula for the new member's value directly. This avoids finding all individual values.

• If a new person joins and average increases: new person's value = old average + (increase x new count)
• If a new person joins and average decreases: new person's value = old average - (decrease x new count)
• If a person leaves and average changes: use old sum minus leaving person's value equals new average x new count
• Key step: always calculate old sum and new sum, then find the unknown

Replacement Type Questions

A member of a group is replaced by a new member and the average changes. These are very popular in Agniveer papers. The logic is simple: find the difference in total sum caused by replacement, then find who was replaced.

• If average increases after replacement: new person's value = old person's value + (increase x total count)
• If average decreases after replacement: new person's value = old person's value - (decrease x total count)
• You do not need individual values — just the change in average and group size

Weighted Average

When two groups with different sizes and averages are combined, the combined average is NOT simply the average of the two averages. You must take into account the size of each group. This appears in questions combining two classes, two trains, two batches etc.

• Combined average = (Sum of group 1 + Sum of group 2) / (n1 + n2)
• Sum of group = average x count for each group
• Combined average is always between the two individual averages
• If both groups same size, combined average = simple average of both group averages

• Using simple average of two averages when combining groups of DIFFERENT sizes — always use weighted average formula.
• In replacement questions, forgetting to multiply the change in average by the total group size, not just 1.
• Confusing 'average increases by 2' with 'new average is 2' — read carefully whether it is the change or the actual new value.
• In consecutive number average, applying formula for 1 to n when the sequence starts from a number other than 1 — use (first + last)/2 instead.
• Not re-reading whether the question asks for the removed person's value or the new average after removal — both types appear.

• SAN formula: Sum = Average x Number. Remember SAN like SAN-dwich. If you have any two, you get the third.
• For replacement: CHANGE x GROUP SIZE = difference in the replaced person value. Think: 1 ripple affects the whole pond (group size).
• Consecutive numbers average: First PLUS Last, DIVIDE by 2. FL/2 — like finding midpoint of a road.
• Weighted average: always go back to SUMS first, then divide. Never average the averages directly unless group sizes are equal.

• Agniveer Army papers repeat the replacement type question almost every year — practice at least 10 such questions before the exam.
• Questions are typically 1-2 steps and solvable in under 60 seconds if you remember Sum = Average x n as your base tool.
• Difficulty is usually easy to moderate — do not skip these. A 2-minute investment here is almost always a correct answer.
• Watch for traps in combined average questions where they give you two groups of DIFFERENT sizes hoping you just average the averages.
• In paper patterns seen recently, at least one question comes from the addition or removal of a person from a group — make this your must-practice type.