Average - Cricket Based Problems on Average (Part 2)

Duration: 10 min

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Inside: a video lesson and guided study material.

Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: Concept and Objectives of Teaching / शिक्षण की अवधारणा एवं उद्देश्य, Levels of Teaching / शिक्षण के स्तर, Learner's Characteristics / शिक्षार्थी की विशेषताएँ, Learning: Nature and Theories / अधिगम: प्रकृति एवं सिद्धांत, Cognition, Memory and Metacognition / संज्ञान, स्मृति एवं अधिसंज्ञान, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Effective Teaching and the Teacher / प्रभावी शिक्षण एवं शिक्षक, Instructional Objectives and Lesson Planning / अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन, Methods of Teaching / शिक्षण विधियाँ, Offline and Online Teaching Methods / ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ, Teaching Support System / शिक्षण सहायक प्रणाली, Evaluation Systems / मूल्यांकन प्रणाली, Sāṃkhya / सांख्य, Individual Behaviour / व्यक्तिगत व्यवहार, Human Resource Management / मानव संसाधन प्रबंधन, Domains of Child Development / बाल्यावस्था में विकास के क्षेत्र, Biological Basis of Emotion / संवेग का जैविक आधार, Upanishads and Bhagavad Gita / उपनिषद और भगवद्गीता, Central and Peripheral Nervous Systems / केन्द्रीय और परिधीय तंत्रिका तंत्र
  2. Paper - 1 | Unit - 2 | Research Aptitude: Research: Meaning, Features and Scientific Method / अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि, Research Paradigms and Approaches / अनुसंधान के प्रतिमान एवं उपागम, Types of Research / अनुसंधान के प्रकार, Variables and Measurement / चर एवं मापन, Methods of Research / अनुसंधान की विधियाँ, Steps of Research / अनुसंधान के चरण, Sampling / प्रतिचयन, Tools and Methods of Data Collection / आँकड़ा संग्रह के उपकरण एवं विधियाँ, Data Analysis and Statistics in Research / आँकड़ा विश्लेषण एवं शोध सांख्यिकी, Thesis and Article Writing / शोध-प्रबंध एवं लेख लेखन, Application of ICT in Research / अनुसंधान में ICT का अनुप्रयोग, Research Ethics / शोध नैतिकता
  3. Paper - 1 | Unit - 3 | Comprehension: Literal Comprehension, Vocabulary and Language in Context, Inferential Comprehension, Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Restoration and Eighteenth-Century Drama, Modern British Fiction, William Shakespeare, Mid-Twentieth-Century and Contemporary British Fiction, American Drama
  4. Paper - 1 | Unit - 4 | Communication: Communication: Meaning, Nature and Process / संचार: अर्थ, प्रकृति एवं प्रक्रिया, Types and Levels of Communication / संचार के प्रकार एवं स्तर, Verbal and Non-verbal Communication / मौखिक एवं अमौखिक संचार, Semiotics and Meaning / संकेत विज्ञान एवं अर्थ, Models and Theories of Communication / संचार के मॉडल एवं सिद्धांत, Effective Communication / प्रभावी संचार, Barriers to Communication / संचार की बाधाएँ, Classroom Communication / कक्षा संचार, Mass Media: Types and Evolution / जनसंचार माध्यम: प्रकार एवं विकास, Mass Media and Society / जनसंचार एवं समाज, Digital and New Media / डिजिटल एवं नव माध्यम, Static General Knowledge / स्थैतिक सामान्य ज्ञान, Morphology and Syntax, Public Health Nutrition / जन स्वास्थ्य पोषण, Newtonian Motion and Stability, GK- Current Affairs / GK- समसामयिकी, Indian Economy / भारतीय अर्थव्यवस्था, Art and Architecture / कला और स्थापत्य, India after Independence / स्वतंत्रता के बाद भारत
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Number System and Simplification / संख्या पद्धति एवं सरलीकरण, Algebra and Ages / बीजगणित एवं आयु, Percentage / प्रतिशतता, Ratio, Proportion, Partnership and Mixtures / अनुपात, समानुपात, साझेदारी एवं मिश्रण, Averages / औसत, Profit, Loss and Discount / लाभ, हानि एवं बट्टा, Simple and Compound Interest / साधारण एवं चक्रवृद्धि ब्याज, Time and Work / समय एवं कार्य, Speed, Time and Distance / चाल, समय एवं दूरी, Mensuration and Geometry / क्षेत्रमिति एवं ज्यामिति, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Series / श्रेणी, Coding-Decoding / कूटलेखन-कूटवाचन, Relationships, Directions and Ranking / संबंध, दिशा एवं क्रम, Arrangements, Puzzles, Clock and Calendar / व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर, Mathematical Foundations, Polity / राजव्यवस्था, जीवनी, Deconstruction, Gender and Queer Theory, Modern British and Irish Poetry, Central Force and Scattering, Chemical thermodynamics, Microscopic techniques, Philosophy of the Constitution / संविधान का दर्शन, Waves, Optics and Charged-Particle Motion, Membrane structure and function, Analysis, Markov Chains, Univariate and Joint Distributions
  6. Paper - 1 | Unit - 6 | Logical Reasoning: Structure of Arguments / युक्ति की संरचना, Terms, Definitions and Uses of Language / पद, परिभाषा एवं भाषा के उपयोग, Categorical Propositions / निरुपाधिक प्रतिज्ञप्तियाँ, Categorical Syllogism / निरुपाधिक न्यायवाक्य, Venn Diagrams / वेन आरेख, Deduction, Induction and Analogy / निगमन, आगमन एवं सादृश्यता, Fallacies / तर्कदोष, Indian Logic: Pramanas / भारतीय तर्कशास्त्र: प्रमाण, Anumana and Vyapti / अनुमान एवं व्याप्ति, Hetvabhasa / हेत्वाभास, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle / अरस्तू, Western Schools of Philosophy / पाश्चात्य दर्शन की विचारधाराएँ, Kant / कांट, Sadhana Paada, Vaiśeṣika / वैशेषिक
  7. Paper - 1 | Unit - 7 | Data Interpretation: Data and Graphical Representation / आँकड़े एवं आलेखीय निरूपण, Data Interpretation: Tables / आँकड़ा निर्वचन: तालिका
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: Computer Fundamentals and Hardware, Memory, Storage and Data Representation, Computer Software, Office Applications, Multimedia and File Formats, Computer Networks, Internet and World Wide Web, Email and Online Communication, Cyber Security, Digital Ethics, IPR and Society, Cloud and Distributed Computing, Emerging Technologies, ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Basics of COA, Introduction to OS, Introduction to CN, Data Communication, Net Layer: IP Addressing, Network Security, Number System, Number Representation, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, Protection of Geographical Indications / भौगोलिक संकेतों का संरक्षण
  9. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystems and Biodiversity / पारितंत्र और जैव विविधता, Human and Environment Interaction / मानव और पर्यावरण की अंतःक्रिया, Development and Environment / विकास और पर्यावरण, Natural Resources – Forests, Water and Soil / प्राकृतिक संसाधन: वन, जल और मृदा, Energy Resources / ऊर्जा संसाधन, Air Pollution / वायु प्रदूषण, Water Pollution and Treatment / जल प्रदूषण और उपचार, Noise Pollution / ध्वनि प्रदूषण, Waste Management / अपशिष्ट प्रबंधन, Environmental Health and Toxicology / पर्यावरणीय स्वास्थ्य और विषविज्ञान, Climate Change and Global Environmental Issues / जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ, Natural Hazards and Disaster Management / प्राकृतिक प्रकोप और आपदा प्रबंधन, Indian Environmental Laws and Policies / भारतीय पर्यावरण कानून और नीतियाँ, International Environmental Agreements / अंतर्राष्ट्रीय पर्यावरण समझौते, Environment / पर्यावरण, Geography / भूगोल, Factory and Industry Systems / कारखाना और उद्योग व्यवस्थाएँ, Earth Materials, Surface Features and Processes, Communicable Diseases and Immunization / संक्रामक रोग और प्रतिरक्षण
  10. Paper - 1 | Unit - 10 | Higher Education System: Education in Ancient India / प्राचीन भारत में शिक्षा, Ancient Centres of Higher Learning / प्राचीन भारत के उच्च शिक्षा केंद्र, Colonial Education Policies and Commissions / औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग, Colonial Colleges, Universities and Reformers / औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक, Education Commissions and Policies after Independence / स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ, National Education Policy 2020 / राष्ट्रीय शिक्षा नीति 2020, Types of Higher Education Institutions / उच्च शिक्षा संस्थानों के प्रकार, Learning Programmes and Academic Credits / अधिगम कार्यक्रम और अकादमिक क्रेडिट, Professional, Technical and Skill-Based Education / व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा, Value Education and Environmental Education / मूल्य शिक्षा और पर्यावरण शिक्षा, Governance, Administration and Financing / शासन, प्रशासन और वित्तपोषण, Regulation, Accreditation and Ranking / उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग
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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a lecture on solving average-related problems, presented by an instructor in a virtual classroom setting. The lecture begins with a problem about Yuvraj Singh's cricket innings, where the average of 40 innings is 50, and the difference between the highest and lowest runs is 172. The average of the remaining 38 innings is 48. The instructor uses the formula for average (Sum = Average × Number) to find the total sum of runs for 40 innings (2000) and for 38 innings (1824). By subtracting these, the sum of the highest and lowest runs is found to be 176. This is combined with the given difference of 172 to form a system of equations: x + y = 176 and x - y = 172, where x is the highest run and y is the lowest. Solving this system yields x = 174 and y = 2, making the highest run 174. The video then transitions to a second problem about the average age of an Indian cricket team. It states that Hardik Pandya is 25, KL Rahul is 3 years older (28), and the average age of the remaining 9 players is x. The total sum of ages is 11x + 25 + 28 = 11x + 53. When Hardik and Rahul are removed, the average of the remaining 9 players is x-1, so their total sum is 9(x-1) = 9x - 9. The equation 11x + 53 = 9x - 9 is solved to find x = -31, which is an impossible age, indicating a data inconsistency. The final problem involves 8 observations with an average of 20, so the total sum is 160. The average of the first two is 15.5, so their sum is 31. The average of the next three is 21.3, so their sum is 64. The sixth observation is 4 less than the seventh, and the seventh is 7 less than the eighth. The instructor sets up the equation 31 + 64 + (x-4) + x + (x+7) = 160, which simplifies to 3x + 98 = 160, leading to 3x = 62 and x = 20.67. The last observation is x+7 = 27.67. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying the word 'AVERAGE' in a futuristic, glowing green font against a dark, digital background. This transitions to a lecture screen where the first problem is presented. The problem states: 'The average runs of 40 innings of Yuvraj Singh is 50. The difference between the highest and lowest runs scored by him in any innings is 172. If the average run of the remaining 38 innings is 48. What is the highest run scored by Yuvraj in any inning?'. The options are (a) 172, (b) 174, (c) 176, (d) Data Insufficient. The instructor begins to solve the problem by writing the formula 'Avg = Sum / n' on the blackboard. He calculates the total sum of runs for 40 innings as 40 * 50 = 2000.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues solving the first problem. He calculates the total sum of runs for the 38 remaining innings as 38 * 48 = 1824. He then subtracts this from the total sum of 40 innings to find the sum of the highest and lowest runs: 2000 - 1824 = 176. He writes the equation 'x + y = 176' on the board, where x is the highest run and y is the lowest. He then uses the given difference, 'x - y = 172'. He adds the two equations: (x + y) + (x - y) = 176 + 172, which simplifies to 2x = 348. He solves for x, getting x = 174. He concludes that the highest run scored is 174, which corresponds to option (b). The instructor then moves to the next problem.

  3. 5:00 – 10:00 05:00-10:00

    The second problem is presented: 'In Indian Cricket team, the age of Hardik Pandya is 25 years. Wicket Keeper KL Rahul is 3 years older than him. If we leave these two from the team, then the average age of the remaining team is decreased by 1 year from the average age of the whole Indian team. What is the average age of the whole team?'. The options are (a) 19, (b) 20, (c) 21, (d) 22. The instructor sets up the problem by letting the average age of the remaining 9 players be 'x'. The total sum of ages for the 11 players is 11x + 25 + 28 = 11x + 53. The sum of the ages of the remaining 9 players is 9(x-1) = 9x - 9. He sets up the equation 11x + 53 = 9x - 9. He simplifies this to 2x = -62, which gives x = -31. He notes that this is an impossible age, indicating a data inconsistency. He then moves to the third problem.

  4. 10:00 – 10:24 10:00-10:24

    The third problem is presented: 'The average of 8 observations is 20. The average of first two and next three observations is 15 1/2 and 21 1/3. If the 6th observation is 4 less than the 7th and 7th is 7 less than 8th observation, then find the last observation?'. The options are (a) 25, (b) 30, (c) 27, (d) Data Insufficient. The instructor calculates the total sum of 8 observations as 8 * 20 = 160. The sum of the first two observations is 2 * 15.5 = 31. The sum of the next three is 3 * 21.333... = 64. He lets the 7th observation be 'x'. Then the 6th is 'x-4' and the 8th is 'x+7'. He sets up the equation: 31 + 64 + (x-4) + x + (x+7) = 160. He simplifies this to 3x + 98 = 160, which gives 3x = 62 and x = 20.67. The last observation is x+7 = 27.67. The video ends with a 'Thanks for Watching' screen.

The video presents a structured lesson on solving average problems, progressing from a straightforward calculation to more complex scenarios involving systems of equations. The core concept is the fundamental formula for average, Sum = Average × Number, which is applied to find total sums and then used to set up equations. The first problem demonstrates how to find the sum of two unknown values (highest and lowest runs) by subtracting the sum of the remaining values from the total sum. This is then combined with a difference to form a system of two linear equations, which is solved to find the individual values. The second problem introduces a logical inconsistency, where the data leads to an impossible negative age, highlighting the importance of checking the validity of solutions. The third problem uses a similar approach, setting up a system of equations based on relationships between variables (observations) to find a specific value. The overall teaching method is to break down each problem into clear, logical steps, using the blackboard to show the derivation process.

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