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Chapter 6 – Statistics And Probability

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You’ll find Statistics and Probability to be two very interesting topics. Not only will you enjoy solving them in school & college, but you’ll find them applicable in real life quite often! Let’s look at them in detail with simplified explanations here.

Probability is all about opportunity. Whereas statistics are all about how, using various methods, we manage different data. In a very simple and intuitive way, it helps to represent complex data. In mathematics Class 9, the introduction of these basics is briefly offered. Concepts like Binomial Probability and Bayes Theorem are taught. 

Today in data technology professions, statistics have a major use. Experts use the figures to make company forecasts. It allows them to predict the possible benefit or loss gained by the enterprise. 

Probability denotes the probability that some unpredictable occurrence would occur. The purpose of this word is to verify the degree to which it is possible that some occurrence may occur. What is the coin toss probability of having a head, for instance? The solution to this question is based on the number of results that are probable. The probability here is that the result will be either head or tail. So, the chance of a head arriving, as a result, is 1/2. 

The chance is the estimate of an event’s possibility of occurring. It tests the event’s certainty. The probability formula is given by; 

P(E) = Number of favourable results/Total results number 

P(E) = n(E)/n n(e)/n (S) 

Here,

N(E) = Event Number beneficial to Event E 

n(S) = Complete number of outcomes

Statistics is a process of gathering and summarizing the results. Stats are used for data processing, whether it is the study of the country’s population or its economy. 

In many disciplines, such as economics, psychology, geology, weather forecasts, etc., statistics have a wide variety. The data for research obtained here may be quantitative or qualitative. There are also two types of quantitative data: discrete and continuous. There is a constant value for discrete data, while continuous data is not fixed data, it has a variety. This definition uses multiple words and formulas. To explain them, see the following table below.

There are several terminologies used in the definitions of probability and statistics, such as: 

1. Random Experiment 

A random experiment is considered an experiment whose results can not be projected until it is noticed. For starters, the outcome is unknown to us when we throw dice randomly. We can get any output that goes from 1 to 6. This experiment is, thus, spontaneous. 

2. Space Sample 

The set of all potential outcomes or effects of a random experiment is a sample space. Suppose, if we randomly throw a dice, then the sample space for this experiment will be all possible dice throwing effects, such as: 

The Space Sample = {1,2,3,4,5,6} 

3. Random Variables

The variables that denote a random experiment’s potential effects are called random variables. They belong to two types: 

  • Random Discrete Variables 
  • Random Continuous Variables 

Only those distinct values which are countable are taken by discrete random variables. 

Whereas an infinite number of potential values might be taken by continuous random variables. 

4. Independent Event 

If the likelihood of one occurrence happening has no effect on the likelihood of another event, then all events are identified as independent of each other. For eg, if you flip a coin and throw dice at the same time, the possibility of having a ‘head’ is independent of the risk of getting a 6 in a dice. A complementary event is a chance when an event occurs if and only if the other event does not occur.

5. Mean 

The sum of the random values of the potential consequences of a random experiment is the mean of a random variable. In simplistic words, it is the compound probability of the random experiment’s potential outcomes, replicated over and over again or a number of times. The expectation of a random variable is often called that. 

6. Expected Value 

The predicted value is a random variable average. For a random experiment, it is the assumed value that is considered. It is sometimes called expectation, first moment, or mathematical expectation. If we roll dice with six faces, for instance, then the predicted value will be the average value of all possible values, i.e. 3.5. 

7. Variance

Basically, the variance shows us how the random variable’s values are distributed around the mean value. The distribution of the space of the sample over the mean is defined.

In this chapter, we learned about the basics of statistics and probability. We learned about their formulas, different terms, and their application in mathematics. We learned about the addition rule of probability, and statistics concepts like compound events.

1. What is the role of probability in statistics? 

Probability is essentially how likely there is to be anything. Whenever we are uncertain about an event’s result, we should ask about the probability of those outcomes-how probable they are. Statistics is called the study of events controlled by chance.

2. What are the 3 types of probability? 

Three main types of probability exist: 

  • Theoretical Probability. 
  • Experimental Probability. 
  • Axiomatic Probability.

3. What does OR mean in probability?

We sometimes want to know the possibility of having one outcome or another. If events are mutually exclusive and we want to know the chance of one occurrence or another, then we should use the law of OR. Mostly seen in conditional probability.

4. What is the formula of probability?

Probability of occurrence of incident P(E) = Number of favorable events/Total number of events.

5. How do you calculate probability and statistics? 

Probability of occurrence of incident P(E) = Number of favorable events/Total number of events.

Formula to calculate statistics

  • Population mean = μ = ( Σ Xi ) / N.
  • Population standard deviation = σ = sqrt [ Σ ( Xi – μ )^2 / N ]
  • Population variance = σ2 = Σ ( Xi – μ )^2 / N.

To learn more about statistics and probability through simple, interactive, and explanatory visualizations, download the MSVgo app.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
  • Management Of Natural Resources
  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
  • Motion in a plane
  • Motion in a straight line
  • Moving Charges and Magnetism
  • Nuclear Energy
  • Nuclei
  • Oscillations
  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
  • Semiconductor Electronics: Materials, Devices and Simple Circuits
  • Simple Machines
  • Sound
  • Sources Of Energy
  • Specific and Latent Heats
  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
  • Chemical Equilibria
  • Chemical Kinetics
  • Chemical Reactions And Equations
  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
  • Chemistry of p-Block elements
  • Chemistry of Transition and Inner Transition
  • Classification of Elements
  • Coordination Compounds
  • Cyanide, Isocyanide, Nitro compounds and Amines
  • Electrochemistry
  • Electrolysis
  • Elements, Compounds and Mixtures
  • Environmental Chemistry
  • Equilibrium
  • Ethers and Carbonyl compounds
  • Haloalkanes and Haloarenes
  • Hydrocarbons
  • Hydrogen
  • Ideal solutions
  • Introduction to Organic Chemistry
  • Ionic equilibria
  • Matter
  • Matter Around Us
  • Matter In Our Surroundings
  • Metallurgy
  • Metals And Non-Metals
  • Mole Concept and Stoichiometry
  • Natural Resources
  • Organic Chemistry – Basic Principles
  • Periodic Classification of Elements
  • Physical and Chemical Changes
  • Physical and Chemical Properties of Water
  • Polymers
  • Preparation, Properties and Uses of Compounds
  • Principles and Processes of Isolation of Elements
  • Redox Reactions
  • Relative Molecular Mass and Mole
  • States of Matter
  • Structure Of The Atom
  • Study of Compounds
  • Study of Gas Laws
  • Study of Representative Elements
  • Surface Chemistry
  • The d-block and f-block elements
  • The Gaseous State
  • The p-Block Elements
  • The Periodic Table
  • The s-Block Elements
  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
  • Biofertilizers
  • Biological Classification
  • Biomedical Engineering
  • Biomolecules
  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
  • Environmental Issues
  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
  • Heredity And Evolution
  • Heredity and Variation
  • How Do Organisms Reproduce?
  • Human Diseases
  • Human Eye And Colourful World
  • Human Health and Disease
  • Human Population
  • Human Reproduction
  • Hygiene
  • Improvement In Food Resources
  • Integumentary System- Skin
  • Kingdom Fungi
  • Kingdom Monera
  • Kingdom Protista
  • Life Processes
  • Locomotion and Movement
  • Microbes in Human Welfare
  • Mineral Nutrition
  • Molecular Basis of Inheritance
  • Morphology of Flowering Plants
  • Neural Control And Coordination
  • Nutrition in Human Beings
  • Organism and Population
  • Photosynthesis
  • Photosynthesis in Higher Plants
  • Plant Growth and Development
  • Plant Kingdom
  • Pollination and Fertilization
  • Pollution; Sources and its effects
  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
  • Reproduction in Organisms
  • Reproductive Health
  • Respiration in Human Beings
  • Respiration in Plants
  • Respiratory System
  • Sexual Reproduction in Flowering Plants
  • Strategies for Enhancement in Food Production
  • Structural Organisation in Animals
  • Structural Organisation of the Cell
  • The Endocrine System
  • The Fundamental Unit Of Life
  • The Living World
  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
  • Calculus – Integrals
  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
  • Geometry – Constructions
  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
  • Geometry – Lines and Angles
  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
  • Hydrogen
  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
  • Metals and Non-metals
  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
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