Demo: Concept of Weighted Average & its role in Alligations

Duration: 14 min

This video lesson is available to enrolled students.

Return to /learn/ZERO-TO-HERO/aptitude/mixture-and-alligation/basic-concepts-and-weighted-average/asset-demo-concept-of-weighted-average-its-role-in-alligations after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence, Cloud Computing
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive introduction to the concept of Weighted Average and its critical role in solving problems related to Mixtures and Alligations. The instructor, Yash Jain, begins by establishing the theoretical foundation of weighted averages, distinguishing them from simple arithmetic means. The core lesson demonstrates that when combining two or more groups with different sizes and values, the overall average is not merely the mean of the individual averages. Instead, it requires calculating the total sum of all values across groups and dividing by the total count of items. The video progresses from concrete numerical examples involving student scores to generalized algebraic formulas, and finally connects these concepts to the Alligation Rule. Key derivations show how the weighted average formula can be rearranged to determine the ratio of weights based on deviations from the mean, providing a powerful shortcut for mixture problems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an introduction to the topic 'CONCEPT OF WEIGHTED AVERAGE' under the broader subject of Mixtures & Alligations. The instructor sets the stage by explaining that this concept is foundational for understanding mixture problems. Visual evidence shows a static title slide with the text 'MIXTURES & ALLIGATIONS' and '- By Yash Jain'. The instructor verbally introduces the core definition, preparing students for a scenario involving two distinct groups. On-screen text begins to appear with labels 'A' and 'B', alongside the specific data point '3 students -> 4', indicating the start of a comparative example to illustrate how group sizes and values contribute to the final average.

  2. 2:00 – 5:00 02:00-05:00

    The instructor formalizes the example by defining Group A as having 3 students with an average of 4, and Group B as having 5 students with an average of 6. The teaching flow shifts to algebraic manipulation, where the standard formula 'Avg = Sum / no.' is presented on screen. The instructor derives the inverse relationship, showing that 'Sum = Avg * no.', which is crucial for finding total values. The screen displays calculations such as '4 * 3 = 12' and '5 students -> 6', establishing the method to find individual sums. This section emphasizes breaking down the problem into components: calculating the sum for each group separately before combining them.

  3. 5:00 – 10:00 05:00-10:00

    This segment demonstrates the calculation of the combined weighted average. The instructor calculates the sum for Group A as 12 and Group B as 30, then adds them to get a total sum of 42. The screen explicitly shows 'Sum3 + Sum5 = 12 + 30' and the division '42 / 8', where 8 is the total number of students. The instructor contrasts this correct method with an incorrect simple average approach, noting that averaging 4 and 6 directly is wrong due to unequal group sizes. The final result '5.25' is derived from the fraction 42/8, which simplifies to 21/4. This concrete example solidifies the definition that weighted average equals total sum divided by total count.

  4. 10:00 – 14:16 10:00-14:16

    The lesson transitions from numerical examples to general algebraic derivation and the Alligation Rule. The screen displays the generalized formula 'x̄ = (n1x1 + n2x2) / (n1 + n2)', showing how to represent any number of groups. The instructor then rearranges this equation to isolate the ratio of weights, deriving 'n1/n2 = (x₂ - x̄) / (x̄ - x₁)'. This derivation connects the weighted average concept directly to Alligation. The video concludes by applying this rule to the previous example, showing differences like '6-5.25' and '5.25-4', which yield a ratio of 0.75 : 1.25, simplified to 3:5. The final slide displays 'Thanks for watching', confirming the completion of the topic.

The video effectively bridges the gap between basic arithmetic and advanced mixture problem-solving techniques. By starting with a tangible example of student scores, the instructor makes the abstract concept of weighting intuitive before moving to algebraic generalization. The derivation of the Alligation Rule from the weighted average formula is a key insight, showing that the ratio of weights is inversely proportional to the deviation of values from the mean. This logical progression ensures students understand not just how to apply formulas, but why they work. The visual cues on screen, such as the step-by-step calculation of sums and the rearrangement of variables, serve as critical revision aids for exam preparation.

Loading lesson…