# Chapter 10 – Statistics

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

Introduction

Statistics and probability are two tools of mathematics discipline concerning the collection, organization, processing, and analysis of quantifiable data. Statistics is limited to the aspects of gathering, managing, and interpreting quantifiable data, whereas probability presents predictions about the occurrence or non-occurrence of events in a varied environment. Statistics and probability are very closely linked due to the presence of quantifiable data and interpretation phenomenon. Additionally, these two mathematical tools also help the students in generating support for an argument with persuasive data.

There are two formulas for the addition rule of probability, pertaining to a probability related to two mutually exclusive events and probability related to two non-mutually exclusive events. The first formula is merely the sum of the probabilities of occurrences or non-occurrence in two events, whereas the second formula adds the aspect of deducting the probability of occurrence of both events simultaneously along with adding the probabilities of occurrences or non-occurrences of two events. This concept can also be understood by videos and materials available on MSVgo.

#### Binomial probability

Binomial probability can be defined as the formulae of sourcing the exact number of successes of getting desired results in a specific number of trials. The formulae for calculating the probability of failure using binomial probability is P(F)= 1 – p (where p is the probability of success, and 1 is the total probability of event occurrence). For more information about binomial probability, check informative content on MSVgo.

#### Bayes’ theorem

Bayes’ theorem is used for finding the probability of occurrence or non-occurrence of an event if other probabilities are certain. The formula for this theorem is P(A|B) =  P(A) P(B|A)/P(B) where P(A|B) details the time event A happens with event B, P(B|A) details the times the event B happens with event A, P(A) is the likeliness of event A happening and P(B) is the likeliness of event B happening. For more understanding, browse videos on MSVgo.

#### Compound events and compound probability

A compound event is a combination of two or more simple events with multiple outcomes. On the other hand, the compound probabilities are the probabilities of events pertaining to multiple outcomes and desires results within specific trails. The key example of compound probability can be rolling an even number on a dice as it has six possible outcomes out of which three are even; thus, the probability of acquiring 2,4 or 6 on dice can be defined as a compound probability. In other words, the compound probability is the mathematical likeliness of two independent events occurring in a specific environment. Generally, the compound probability is derived by multiplying the probability of first event occurrence with the probability of second event occurrence. However, it is to be noted that the formula for calculating the compound probability tends to differ on the basis of the sort of compound event being mutually exclusive and mutually inclusive. For further clarification on this concept, check videos on MSVgo.

#### Complementary events

In probability theory, the complement of occurrence of any event is the probability of that event not occurring. For instance, the complement of event A is the event NOT A. Denotation of the complimentary event is A’ or Ac. If event A is it will rain today, the complement event A’ will be; it will not rain today. The commonality among complementary events is that they are mutually exclusive and exhaustive. However, if the events are mutually exclusive, they cannot occur simultaneously; however, as they are exhaustive, the sum of their probabilities needs to be 100%. For more understanding about the concept of complementary events, browse videos on MSVgo.

#### Conditional probability

Conditional probability concerns the probability of occurrence of an event along with a relationship to one or multiple other events. For instance, if event A is of raining outside with a probability of 0.3 and event B is going outside with a probability of 0.5. The conditional probability will be applied when going outside is subjected to raining outside. The formula of conditional probability is P(B|A) = P (A and B) / P(A) or P(B|A) = P(A∩B) / P(A). Conditional probability is generally used in the diversified fields of calculus, politics, and insurance. This concept can also be understood by videos and materials available on MSVgo.

#### Coin toss probability

When a coin is flipped, there are two possible outcomes, which are either head or tail, with a 50 percent probability for each. The probability for the occurrence of the head on top or tail on top when a coin is flipped is always 50-50 due to the presence of only two alternatives. For more information and questions related to coin toss probability, browse the videos on MSVgo.

Statistics and probability are the two branches of mathematics that are concerned with practices that govern occurrences and non-occurrences of random events by means of collecting, analyzing, interpreting, and presenting numerical data in an efficient way. Probability provides the logic of uncertainty for predicting events so that actions can be taken accordingly in real-time.

#### FAQs

What is probability and statistics in math?

Probability and statistics are the branches of mathematics concerned with laws and practices of governing random events by collecting, analyzing, interpreting, and displaying numerical data.

What is the role of probability in statistics?

Probability concerns with conducting an analysis of chances, games, genetics, and predictions pertaining to everyday activities and presenting interpretation in numerical data on the basis of the same.

What is the purpose of probability?

Probability concerns with detailing the likelihood of the occurrence of some event or something in varied aspects such as a game of chances or weather pattern predictions. The likeliness of an event occurring or not occurring tend to help individuals in varied ways.

What are the four types of probability?

Classical, empirical, subjective, and axiomatic are the four types of probability.

What is statistics in math?

Statistics is the branch of mathematics that concerns the collection, analysis, and interpretation of numerical and quantitative data. Statistics presents numeric data using graphs for the easy and efficient understanding of the processing data pertaining to the specific topic, environment, condition, or situation.

### 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
• 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
• 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
• 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 – 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
• 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
• 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

• 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