Average is one of the most fundamental topics in IBPS PO Quantitative Aptitude, appearing both as direct questions and as a component within Data Interpretation sets. Typically, 1–3 questions in Prelims test average concepts, either standalone or combined with age problems and word scenarios.
The concept is straightforward, but IBPS PO tests your ability to handle weighted averages, changes when elements are added or removed, and age-based variations under time pressure. Mastering average shortcuts—especially the deviation method—can save 30–60 seconds per question, which compounds significantly across the exam.
Students who score well treat average not just as a formula but as a balancing concept: the average is the "balancing point" of a data set, and deviations above and below it must sum to zero.
Key Concepts
**Simple Average** = Sum of observations ÷ Number of observations. This is the arithmetic mean.
**Weighted Average**: When groups have different sizes, multiply each group's average by its weight (count), sum them, then divide by total weight. You cannot simply average the averages.
**Deviation Method**: Instead of calculating full sums, assume an approximate average, find deviations from it, and adjust. This is faster for large numbers.
**Effect of Adding/Removing Elements**: When a new value is added, the change in total equals (new value − old average) if the count increases by 1. Similarly, removing a value shifts the average based on how far that value was from the old average.
**Age-Based Averages**: The average age of a group increases by 1 for every year that passes (assuming no one joins or leaves). When someone joins or leaves, recalculate using the total age concept.
**Sum = Average × Count**: This relationship is the backbone. Most problems become easier when you work with totals rather than averages directly.
**Replacement Problems**: When one element replaces another, the change in sum = (new element − replaced element). The average changes by this difference ÷ count.
Formulas / Key Facts
**Basic Formula** Average = Sum of all values ÷ Number of values Sum = Average × Number of values
**Deviation Method** Assumed mean = A Actual Average = A + (Sum of deviations from A ÷ Number of values)
**Change in Average (Element Added)** New Average = (Old Sum + New Value) ÷ (Old Count + 1) Change in Average = (New Value − Old Average) ÷ New Count
**Change in Average (Element Removed)** New Average = (Old Sum − Removed Value) ÷ (Old Count − 1)
**Replacement Formula** Change in Sum = New Value − Old Value Change in Average = (New Value − Old Value) ÷ Count
**Age Problems** After T years, average age of the same group increases by T. Total present age = Average present age × Number of persons
Worked Examples
### Example 1: Basic Average with Addition
**Problem**: The average of 5 numbers is 42. If a sixth number is added, the average becomes 44. Find the sixth number.
**Solution**:
Old sum = 5 × 42 = 210
New sum = 6 × 44 = 264
Sixth number = 264 − 210 = **54**
*Shortcut*: The sixth number exceeds the new average by enough to raise all 6 values. It must "donate" 2 to each of the original 5 numbers (since average rose by 2), so it contributes 44 + (5 × 2) = 44 + 10 = 54.
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### Example 2: Weighted Average
**Problem**: Class A has 30 students with an average score of 60. Class B has 20 students with an average score of 75. Find the combined average.
**Solution**:
Total marks of A = 30 × 60 = 1800
Total marks of B = 20 × 75 = 1500
Combined total = 1800 + 1500 = 3300
Total students = 30 + 20 = 50
Combined average = 3300 ÷ 50 = **66**
*Note*: The combined average (66) is closer to 60 than to 75 because Class A has more students—this is the "weighted pull."
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### Example 3: Age-Based Average
**Problem**: The average age of a family of 4 members is 25 years. A baby is born, and 3 years later, the average age of the family becomes 22 years. What was the age of the baby when born?
**Solution**:
Total age of 4 members initially = 4 × 25 = 100 years
After 3 years, each of the 4 original members ages by 3: their total = 100 + 12 = 112 years
Baby's age after 3 years = 3 years (since born at time zero, now 3 years old)
Total age of 5 members after 3 years = 112 + 3 = 115 years
Average should be = 115 ÷ 5 = 23 years
Wait—the problem states the average becomes 22. Let me re-read.
Actually, let the baby's age at birth be B.
After 3 years, total age of family = (100 + 12) + (B + 3) = 115 + B
New average = (115 + B) ÷ 5 = 22
115 + B = 110
B = −5 (This is impossible, indicating the problem likely means something different)
**Re-interpretation**: If the average *drops* to 22, likely the baby was born and 3 years have NOT passed for calculation—or there's a different setup. In IBPS PO, always verify problem logic. For standard problems:
**Corrected typical problem**: Average of 4 members is 25. Baby born now. New average of 5 members is 22. Baby's age = ?
Old total = 100
New total = 5 × 22 = 110
Baby's age = 110 − 100 = **10 years**? That's also odd for a baby.
Such contradictions in practice sets mean re-checking is essential. **Baby's age at birth = 0**, so: 5 × new average = 100 + 0 = 100, new average = 20. If asked this way, answer = 0.
Common Mistakes
**Averaging the averages directly**: Students often find (60 + 75) ÷ 2 = 67.5 for weighted average problems. → Always weight by group size first.
**Forgetting time progression in age problems**: When "3 years later" is mentioned, every existing member ages by 3. → Add (3 × number of members) to the old total before any other calculation.
**Confusing count change**: When adding an element, the new count is n+1, not n. → Write down the new count explicitly to avoid division errors.
**Ignoring direction of change**: If a person leaving causes the average to increase, that person's value was below the original average. → Think logically about whether the removed/added value pulls the average up or down.
**Calculation errors with large numbers**: Using full sums (like 3847 + 3921 + ...) wastes time and invites errors. → Use the deviation method with an assumed mean close to the expected average.
Quick Reference
Sum = Average × Count — convert averages to totals first.
Weighted average lies closer to the group with more members.
Adding a value above the current average raises the average; below lowers it.
Age problems: total age of a fixed group increases by (n × years passed).
Change in average = (Difference introduced) ÷ (New count).
Deviation method: Assume a convenient mean, work with small differences.
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