Average

Overview

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

**Weighted Average** Weighted Average = (n₁ × A₁ + n₂ × A₂ + ... + nₖ × Aₖ) ÷ (n₁ + n₂ + ... + nₖ)

**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