Average Tricks for SSC CGL: The Short Answer
Average = sum of observations ÷ number of observations. Almost every average question in SSC CGL becomes easy if you work with totals instead of averages: multiply each average by its count, add or subtract, then divide once at the end. For "average increases when someone joins or is replaced" questions, use the shortcut new value = old value (or old average) + number of people × change in average.
Key takeaway for SSC: SSC CGL, CHSL, MTS and GD ask 1 to 2 average questions in maths, and bank Clerk exams ask them as arithmetic word problems. The eight question types below (natural numbers, inclusion, replacement, wrong entry, overlapping groups, cricket innings, weighted average and age at an earlier time) cover nearly every exam question. Every answer here was checked in Python.
Average links closely to ratio and percentage, so pair this note with our ratio and proportion for SSC CGL and mixture and alligation questions notes.
Average Formula (Basic and Weighted)
| Find | Formula |
|---|---|
| Average | Sum ÷ Number of items |
| Sum | Average × Number of items |
| Weighted average | (n₁a₁ + n₂a₂ + …) ÷ (n₁ + n₂ + …) |
Example 1: Find the average of 45, 52, 38, 61 and 54.
Sum = 250, so average = 250 ÷ 5 = 50.
Deviation trick: assume an average (say 50) and add the mean of the deviations. Deviations: −5, +2, −12, +11, +4 → total 0. So the average is exactly 50. This is faster for large numbers like 4,512, 4,498, 4,505.
Average of Natural, Even and Odd Numbers (Formula Table)
| Series | Average |
|---|---|
| First n natural numbers | (n + 1) ÷ 2 |
| First n even numbers | n + 1 |
| First n odd numbers | n |
| Squares of first n natural numbers | (n + 1)(2n + 1) ÷ 6 |
| Cubes of first n natural numbers | n(n + 1)² ÷ 4 |
| Any consecutive numbers (or any arithmetic series) | (first + last) ÷ 2 |
Examples: average of the first 50 natural numbers = 25.5; first 20 even numbers = 21; first 15 odd numbers = 15; squares of 1 to 10 = 38.5; numbers from 12 to 30 = 21.
Average Tricks When a Person Joins or Leaves
If a new person joins a group of n and the average rises by d:
New person's value = new average + n × d (or old average + (n + 1) × d).
Example 2: The average age of 30 students is 14 years. When the teacher's age is included, the average rises by 1 year. Find the teacher's age.
New average = 15. Teacher = 15 + 30 × 1 = 45 years.
Check: 31 × 15 − 30 × 14 = 465 − 420 = 45. ✔
If a person leaves and the average falls, use the same idea with totals: leaving value = old total − new total.
Replacement Questions in Average (Shortcut Formula)
When one member is replaced and the average of n changes by d:
New member = old member ± n × d (+ if the average rises, − if it falls).
Example 3: The average weight of 8 men increases by 2.5 kg when a new man replaces one who weighs 65 kg. Find the new man's weight.
New man = 65 + 8 × 2.5 = 85 kg.
Example 4: The average of 25 numbers is 18. If 42 is replaced by 17, find the new average.
New total = 450 − 42 + 17 = 425. New average = 425 ÷ 25 = 17. (Shortcut: change = (17 − 42) ÷ 25 = −1.)
Wrong Entry (Misread Value) Average Questions
Correct average = old average + (correct value − wrong value) ÷ n
Example 5: The average of 40 numbers was found to be 50. Later it was found that 64 had been read as 46. Find the correct average.
Correct average = 50 + (64 − 46) ÷ 40 = 50 + 0.45 = 50.45.
Overlapping Groups (First Few and Last Few)
When the first few and last few groups share one item:
Shared item = (sum of first group) + (sum of last group) − total sum
Example 6: The average of 11 results is 60. The average of the first 6 is 58 and of the last 6 is 63. Find the 6th result.
6th = 6 × 58 + 6 × 63 − 11 × 60 = 348 + 378 − 660 = 66.
Example 7 (three people): The average weight of A, B and C is 45 kg. The average of A and B is 40 kg and of B and C is 43 kg. Find B's weight.
B = 2 × 40 + 2 × 43 − 3 × 45 = 80 + 86 − 135 = 31 kg.
Cricket Innings Average Questions (Batting Average Trick)
Example 8: A batsman's average is 32 after 10 innings. How many runs must he score in the 11th innings to raise his average by 4?
Runs = new average × 11 − old total = 36 × 11 − 32 × 10 = 396 − 320 = 76.
Shortcut: runs needed = new average + (old innings × increase) = 36 + 10 × 4 = 76. ✔
Example 9: A batsman scores 87 in his 17th innings and his average rises by 3. Find his new average.
Let the old average be a. Then 16a + 87 = 17(a + 3), so a = 36 and the new average = 39.
Shortcut: new average = score − (old innings × increase) = 87 − 16 × 3 = 39.
Weighted Average and Age Average Questions
Example 10 (weighted average): Section A has 30 students with average marks 60, and Section B has 20 students with average 70. Find the combined average.
(30 × 60 + 20 × 70) ÷ 50 = 3,200 ÷ 50 = 64.
Example 11 (age at an earlier time): The average age of a family of 5 is 24 years. The youngest member is 6 years old. Find the average age of the family at the time of the youngest member's birth.
Six years ago, the other 4 members' total age was (5 × 24) − 6 − 4 × 6 = 120 − 6 − 24 = 90. Average = 90 ÷ 4 = 22.5 years.
Formula: [n × average − youngest's age − (n − 1) × youngest's age] ÷ (n − 1) = (120 − 5 × 6) ÷ 4 = 22.5. ✔
Average Tricks for SSC CGL (Quick Revision Table)
| Type | Shortcut |
|---|---|
| Person joins, average rises by d | Value = new avg + n × d |
| Replacement, average changes by d | New = old ± n × d |
| Wrong entry | Correct avg = avg + (correct − wrong) ÷ n |
| Overlapping groups | Shared = sum₁ + sum₂ − total |
| Cricket, runs to raise avg by d | Runs = new avg + old innings × d |
| Cricket, find new average | New avg = score − old innings × d |
| Natural numbers 1 to n | (n + 1) ÷ 2 |
| Arithmetic series | (first + last) ÷ 2 |
Common Mistakes in Average Questions
- Averaging averages. Two groups of different sizes need the weighted formula.
- Using n instead of n + 1 when a new person joins.
- Forgetting the direction of the wrong-entry correction (correct − wrong).
- Ignoring time in age questions. Everyone's age changes by the same number of years.
- Rounding too early. Keep fractions until the final step.
Average Questions for SSC CGL (Practice Set with Answers)
- Find the average of the first 100 natural numbers. Answer: 50.5. (100 + 1) ÷ 2.
- The average age of 20 students is 15 years. When the teacher is included, the average becomes 16. Find the teacher's age. Answer: 36 years. 16 + 20 × 1.
- The average of 50 numbers is 36. Later, 84 was found to have been recorded as 48. Find the correct average. Answer: 36.72. 36 + 36 ÷ 50.
- The average of 9 numbers is 48. The average of the first 5 is 45 and of the last 5 is 52. Find the 5th number. Answer: 53. 225 + 260 − 432.
- A batsman's average after 6 innings is 25. How many runs must he score in the 7th innings to make his average 26? Answer: 32. 7 × 26 − 6 × 25.
- The average weight of 10 people rises by 3 kg when a new person replaces one weighing 50 kg. Find the new person's weight. Answer: 80 kg. 50 + 10 × 3.
- The average of three numbers is 28 and the average of the first two is 30. Find the third number. Answer: 24. 84 − 60.
- A batsman scores 98 in his 20th innings and his average rises by 2. Find his new average. Answer: 60. 98 − 19 × 2.
- In a class, 40 boys have an average score of 12 and 60 girls have an average of 18. Find the class average. Answer: 15.6. (480 + 1,080) ÷ 100.
- Find the average of all numbers from 21 to 59. Answer: 40. (21 + 59) ÷ 2.
For timed practice, take the SSC CGL Average Mock Test 01 and the SSC CGL Average Mock Test 02.
Average Tricks FAQs
What is the formula of average?
Average = sum of all observations ÷ number of observations. If you know the average, the sum is average × number of observations.
How do you solve average questions quickly?
Convert every average into a total (average × count), do the addition or subtraction with totals, and divide only at the end. Use shortcuts like "new value = new average + n × change" for joining and replacement questions.
What is the average of the first n natural numbers?
(n + 1) ÷ 2. For example, the average of 1 to 50 is 25.5 and of 1 to 100 is 50.5.
How do you find the correct average after a wrong entry?
Correct average = wrong average + (correct value − wrong value) ÷ number of items.
How many average questions come in SSC CGL?
Usually 1 question in SSC CGL Tier 1 maths, sometimes 2. SSC CHSL, MTS and GD ask 1 to 2, and bank Clerk exams include average in arithmetic word problems.
What is a weighted average?
It is the average of groups of different sizes: (n₁a₁ + n₂a₂) ÷ (n₁ + n₂). It is not the simple average of the two group averages unless the groups are equal.
Practice Next
- Topic tests: SSC GD Average Mock Test 02 and RRB ALP Maths Mock Test 02.
- Mock tests: SSC CGL Average Mock Test 01, SSC CGL Average Mock Test 02, SSC CGL Average Mock Test 03 and SSC CHSL Average Mock Test 01.
- Related notes: ratio and proportion for SSC CGL, mixture and alligation questions for bank exams, age problems for bank exams and statistics formulas for SSC CGL.
- Exam details: SSC CGL 2026 and SSC CHSL 2026.
- Browse all study notes.