Average Questions for SSC GD

What is Average

Average means distributing a total equally among all members. Think of it like sharing a plate of rotis equally at a table — if 4 people share 20 rotis, each gets 5. That number 5 is the average. In maths, average is always Total divided by Count.

• Average = Sum of all values divided by number of values
• Sum = Average multiplied by Number of items
• Number of items = Sum divided by Average
• If all values are equal, the average equals that value
• Average always lies between the smallest and largest value in the group

Average of Consecutive Numbers

For consecutive numbers, consecutive even numbers, or consecutive odd numbers, the average is simply the middle value. If the count is even, the average is the mean of the two middle values. This is a huge time saver — no need to add all numbers.

• 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 consecutive numbers the average equals the middle number

Adding or Removing a Member Changes the Average

A very common SSC GD pattern: a new person joins a group or leaves it, and the average changes. The trick is to use the SUM. Old sum = old average x old count. New sum = new average x new count. The difference in sums tells you the value of the person who joined or left.

• New person joins: New value = new average x new count minus old average x old count
• Person leaves: Removed value = old average x old count minus new average x new count
• If new average is higher than old average, the new person has a higher value than old average
• If new average is lower, the new person dragged the average down
• This logic works for runs in cricket, marks in class, age of team etc.

Replacement Type Questions

One member is replaced by another and the average changes. This is a favourite SSC pattern. Formula: the difference in average times the total count equals the difference between the new person and the old person. Think of it as: each of the n members feels the effect of the swap.

• If average increases after replacement: new person value = old person value + (increase in average x total count)
• If average decreases after replacement: new person value = old person value - (decrease in average x total count)
• Total count stays the same in replacement — only the sum changes
• The change in total = change in average x n

Weighted Average

When two groups with different averages are combined, the combined average is not a simple average of the two group averages. It depends on how many members are in each group. Heavier group (more members) pulls the combined average towards itself.

• Combined Average = (Sum of group 1 + Sum of group 2) / (n1 + n2)
• Sum of group = average of group x number in group
• Combined average lies between the two group averages always
• If both groups are equal in size, combined average = simple average of the two

• Using old count instead of new count after adding or removing a member — always update n first.
• Taking simple average of two group averages when combining groups — you must weight by group size.
• Forgetting that average of first n odd numbers is exactly n, not n+1 — mix-up with even numbers formula.
• In replacement questions, applying the change in average to the wrong person — the formula gives the NEW person's value, not the old one.
• Dividing by wrong n when a member leaves — count goes down by 1, not stays same.

• SAN rule: Sum equals Average times N. Always find sum first before anything else — sum is your best friend.
• For consecutive numbers think MIDDLE — the average always sits at the middle of the sequence.
• Replacement memory trick: DRANCO — Difference in Average times N plus old value equals New value Coming in.
• Visualise a seesaw for weighted average — the heavier side (more members) pulls the balance point (combined average) closer to itself.

• SSC GD typically asks 1 to 2 average questions. Replacement and add/remove type are more common than basic formula questions — practise those two patterns most.
• Questions are usually 1 to 2 steps. If your calculation is going beyond 3 steps, you likely picked the wrong approach — go back to Sum = Avg x N.
• Numbers in SSC GD average questions are small and clean. If you are getting decimals midway in a basic question, recheck your count n.
• Average of consecutive number series appears in the number system section sometimes — know the shortcut (first+last)/2 to save 30 seconds.
• Time target: solve each average question in 45 to 60 seconds. If it takes longer, mark and move — do not let one question eat your time.