Average Guide & Practice
Learn average formula, weighted average, group average, average speed, and DI-based average problems with solved examples and free mock tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.
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1. Fundamentals & Definitions
- Average: The central value of a group of numbers, representing the equal distribution of a total sum across all terms. It is calculated by dividing the sum of observations by the number of observations.
- Sum of Observations: The total value obtained by adding all the individual items in a dataset. It can be calculated by multiplying the average by the number of observations.
- Number of Observations: The total count of items in the dataset.
2. Core Concepts & Formulas
Main Formulas
| Concept | Formula / Rule |
|---|---|
| Simple Average | Average = Total Sum / Number of Terms |
| Total Sum | Total Sum = Average x Number of Terms |
| New Average after Adding a value 'x' | New Average = (Old Total + x) / (n + 1) |
| New Average after Removing a value 'x' | New Average = (Old Total - x) / (n - 1) |
| Change in Average due to one term | Change in Average = Change in Total / Number of Terms |
| Corrected Average | Correct Average = Old Average +/- (Error Difference / Number of Terms) |
| Average of Consecutive Numbers | Average = (First Term + Last Term) / 2 |
| Average of First 'n' Odd Numbers | Average = n |
| Average of First 'n' Natural Numbers | Average = (n + 1) / 2 |
| Average Speed (for Equal Distance) | Average Speed = 2xy / (x + y) |
| Weighted Average | Weighted Average = Sum of (Value x Weight) / Sum of Weights |
Types of Average Problems
| Unit | Subtopics to Study | Common Question Formats |
|---|---|---|
| Basic Average | Definition, average formula, sum formula | Find the average, total sum, or a missing term. |
| Adding/Removing Value | How the average changes when values are added or removed | Find the excluded number, added number, or the new average. |
| Replacement/Correction | Correcting a wrong entry or replacing an old value | Find the corrected average or the impact of the correction. |
| Consecutive Numbers | Average of consecutive natural, even, or odd numbers | Use the middle term or the (first + last)/2 formula. |
| Group Average | Merging two or more groups with different averages | Find the combined average or a missing group's value/average. |
| Weighted Average | Datasets where different quantities have different weights | Calculate average marks, salary, price, or mixture values. |
| Average Age | Calculating average age of a group, after/before 'n' years, or when a new member joins | Find the family/group average age. |
| Average Speed | Calculating average speed over a journey | Use harmonic mean for equal distances with different speeds. |
| Average in Data Interpretation (DI) | Extracting data from tables, bar charts, or pie charts | Calculate average sales, marks, population, etc., from the given data. |
Typical Exam Weightage
| Exam | Typical Questions |
|---|---|
| SSC (CGL / CHSL / MTS) | 1–2 questions |
| Banking (IBPS / SBI) | 1–2 questions |
| Railways (RRB) | 1 question |
A quick-scoring topic when you know the weighted-average shortcut — rarely requires more than basic formula application.
Figures are typical ranges based on recent-year patterns, not a guarantee for any specific upcoming paper — always cross-check against the latest official syllabus and previous-year papers for Average.
Solved Examples
Question: Find the average of the first 10 odd numbers.
Question: The average of 5 numbers is 28. If one number is excluded, the average becomes 26. Find the excluded number.
Question: The average marks of 25 boys is 60 and the average marks of 15 girls is 70. Find the average marks of the entire class.