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Averages for IBPS Clerk

Average = total ÷ number, and most average questions become easy once you work with totals. The assumed-mean method, adding or removing a value, replacement, weighted averages, corrected averages and consecutive numbers, each with why it works, six worked examples and eight practice questions.

2 Oct 2026 5 min read

In this guide
  1. The total method, and why it works
  2. The assumed-mean method
  3. Shortcut results
  4. Weighted average
  5. Worked examples
  6. Common mistakes
  7. Practice
  8. What to do next

Average = sum of values ÷ number of values. The single most useful habit in this topic is to turn every average into a total before you do anything else. Averages are awkward to add, subtract or compare. Totals are not.

Averages appear in clerk papers as short word problems, and even more often inside DI, where "average sales per branch" or "average over five years" is a standard question. The methods below take each type to under 40 seconds.

The total method, and why it works

Total = average × number. When something changes in the group (a value is added, removed, replaced or corrected), compare the totals before and after. The difference is the value you are looking for.

This works because an average is only the total shared equally. Every change to the group is a change to the total first, and the average then follows.

The assumed-mean method

To average numbers that are close to each other, pick a round number near the middle, find each value's deviation from it, and average the deviations.

Average = assumed mean + (sum of deviations ÷ number).

Why: if each value is A + dᵢ, the total is nA + (sum of dᵢ), and dividing by n gives A + (sum of dᵢ)/n. You add small numbers instead of large ones.

Shortcut results

SituationResult
Consecutive numbers (or any evenly spaced list)Average = middle term, or the mean of the first and last
First n natural numbers(n + 1) ÷ 2
First n odd numbersn
First n even numbersn + 1
One member replaced, average of n rises by dNew member = old member + n × d
A new member joins n, average rises by dNew member = old average + (n + 1) × d

The replacement rule follows from the total method. If the average of n members rises by d, the total rises by n × d. The only change is the swap, so the newcomer must bring exactly n × d more than the person who left.

Weighted average

When two groups of different sizes are combined, the overall average is not the simple mean of the two averages. Use totals: (n₁ × a₁ + n₂ × a₂) ÷ (n₁ + n₂). The larger group pulls the result towards its own average.

Worked examples

Example 1. Find the average of 47, 52, 55, 49 and 57.

  1. Assume 50. Deviations: −3, +2, +5, −1, +7. Sum = +10.
  2. Average = 50 + 10 ÷ 5 = 52. Check: total 260, and 260 ÷ 5 = 52.

Example 2. The average age of 20 students is 15. When the teacher's age is included, the average becomes 16. Find the teacher's age.

  1. Totals: before 20 × 15 = 300, after 21 × 16 = 336.
  2. Teacher = 36.
  3. Shortcut: new member = old average + (n + 1) × d = 15 + 21 × 1 = 36.

Example 3. The average weight of 8 people rises by 2 kg when a person weighing 60 kg is replaced by a new person. Find the new person's weight.

  1. The total rises by 8 × 2 = 16 kg.
  2. New person = 60 + 16 = 76 kg.

Example 4. Section A has 30 students with an average of 60 marks. Section B has 20 students with an average of 70. Find the average of all 50.

  1. Totals: 30 × 60 = 1,800 and 20 × 70 = 1,400.
  2. Average = 3,200 ÷ 50 = 64.
  3. The simple mean of 60 and 70 is 65. The answer is lower because the larger section has the lower average.

Example 5. The average of 25 observations was found to be 40. Later it was noticed that a value of 64 had been read as 46. Find the correct average.

  1. The total was understated by 64 − 46 = 18.
  2. Correct average = 40 + 18 ÷ 25 = 40.72.

Example 6. The average of five consecutive odd numbers is 27. Find the largest.

  1. For evenly spaced numbers, the average is the middle term, so the middle is 27.
  2. The numbers are 23, 25, 27, 29, 31. Largest = 31.

Common mistakes

  • Averaging two averages when the groups are of different sizes.
  • In replacement questions, using n + 1 instead of n. The group size does not change in a replacement.
  • In "one more joins" questions, using n instead of n + 1.
  • Correcting the average by the wrong value instead of dividing the error by the number of observations.

Practice

Set a 5-minute timer.

  1. Average of 10, 20, 30, 40, 50?
  2. The average of 6 numbers is 20. A seventh number is added and the average becomes 22. Find the seventh number.
  3. The average age of 10 people rises by 1 year when a person aged 30 is replaced. Find the new person's age.
  4. Average of the first 20 natural numbers?
  5. A player averages 40 runs over 10 innings. How many runs are needed in the 11th innings to raise the average to 42?
  6. Find the average of 68, 73, 71, 66 and 77 using an assumed mean.
  7. Group A has 40 employees with an average salary of ₹25,000; group B has 60 with an average of ₹30,000. Find the overall average.
  8. The average of 30 values is 50. A value of 85 was wrongly recorded as 58. Find the correct average.

Answers:

  1. 30. Evenly spaced, so it is the middle term.
  2. 34. New total 7 × 22 = 154; old total 120.
  3. 40. 30 + 10 × 1.
  4. 10.5. (20 + 1) ÷ 2.
  5. 62. Needed total 11 × 42 = 462; current 400. Shortcut: 40 + 11 × 2.
  6. 71. Assume 70; deviations −2, +3, +1, −4, +7 sum to 5; 70 + 5 ÷ 5.
  7. ₹28,000. (40 × 25,000 + 60 × 30,000) ÷ 100 = 28,00,000 ÷ 100.
  8. 50.9. Error = 85 − 58 = 27; 50 + 27 ÷ 30.

What to do next

  • Rework each practice question using totals only, then again using the shortcut table, and compare times.
  • Do eight average questions a day for a week, mixing replacement and weighted types.
  • Use the same total method in problems on ages, where "average age" questions are common.
  • Practise averages inside data interpretation sets.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Institute of Banking Personnel Selection website .

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