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Chapter 6 – Statistics

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

Introduction

Statistics is the branch of mathematics that deals with data collection and statistical representation of a particular analysed data. This mathematics branch deals with all the study, analysis, collection, representation, interpretation, organisation and presentation of the data in histograms, pie charts, bar graphs and other formats.

Before we start with the data type, we need to understand what exactly data means. We can define Data as the collection of facts and figures that can help you conclude. Apart from the facts, data can be the collection of words, numbers, observation and measurements. Here are the types of data:

  • Qualitative Data: The first category of data is the qualitative data related to the description of a person, thing or entity. 
  • Quantitative Data: The second is quantitative data that is numerical information about a thing or entity. 
  • Discrete data: This is the category of data with a particular fixed value and can be counted. 

Continuous Data: All the data with a range and no fixed value is categorised under continuous data. One can measure the data.

When it comes to data representation, we already know many different ways like Pie charts, Bar charts, etc. Every data can be represented differently. Here are some of the common ones. 

  • Histogram

A histogram is something similar to the bar graph but a complex version of it. In a histogram, you have the X and Y axis that has rectangles in the entire diagram. Each rectangle’s length or proportion shows the frequency of a particular variable whose class interval is depicted by the rectangles’ width. There should be no gaps between bars as it represents the continuous group data. 

  • Frequency distribution

Amongst all the representations, the first one that we learn at a young age is the frequency distribution. It is a collection of data values of a variable which is commonly represented as “f”. The table is made using the set of data and arranging them in ascending order of their frequency or magnitude.

  • Ogive

Ogive, also known as a cumulative frequency curve, is also an essential part of this chapter. It is the representation of the cumulative frequency distribution of any given grouped data. It is also termed as one of the most efficient ways to analyse data to derive results.

One of the essential elements of the statistics chapter is mean. The arithmetic mean of any data is found using the method:

Mean= Sum of all observation/ Total number of observation

Or Mean x¯ = ∑x/n

X bar is the arithmetic mean in the formula, and the sum of all the observations divided by the total number of observations gives the mean.

The Median of the set of data is defined as the mid-value or middlemost observation of given data. The condition that it needs to satisfy is that the data should be arranged in ascending order. When finding the median, there are two formulas that we use.

When the total number of observations is odd. The formula that is used when n is odd:

Median = [(n+1)/2]th observation

When the total number observations is even the formula that has to be used is:

Median = [(n/2) + (n/2+1)] / 2

Therefore, when you are asked to find the median of a set of observations, you should count the total number of observations first. 

This formula is used to get the midpoint of all the observations when the number of observations is more. In this, n is the variable that depicts the total number of observations given in the question. Just insert the value and get the answer.  

There is another way by which one can find the median. This formula has to be used when you get a table consisting of grouped data.

Median= l+[ (n/2-c)/f ]xh

or 

Median= Mean/{(n/2+1)th +(n/2)th}observations

The third and another essential calculation that is asked to do in statistics is to find the mode. It is defined as the value that has the most frequency in a table. For ungrouped data, it is easy to find the mode as you need to check the value given the most number of times. But when it comes to Grouped data, things do change. 

In ungrouped data, the formula to determine mode will be,

Mode= l + [ (fm – f1) / ( 2fm- f1 – f2) ] x h

In this chapter, students learn about the basics of statistics, formulas for mean, median, mode. We learned the types of data representation which includes the use of histograms, frequency distribution and ogive. We also saw the different types of data we study in statistics.

  1. What is statistics?
    Statistics is the branch of mathematics that deals with data collection and statistical representation of a particular analysed data.
  2. What are all types of data representations called statistics?
    When represented as a pie chart, bar graph, histogram, line graph, pictographically, or frequency distribution, a data collection is called statistics.
  3. What examples can you give of collecting data from day-to-day life?
    Increase in our country’s population in the last two decades, the number of tables and chairs in a classroom.

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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
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  • 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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