6.1.2
Statistics Key Terms
Statistics Key Terms
Statistics Key Terms
Statistics is about estimating information about the whole group by using a smaller group.
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Population and sample
Population and sample
- A whole group is called a population and a smaller group within the population is called a sample.
![Illustrative background for Sample needs to be representative](https://image-v2.cdn.app.senecalearning.com/2018-03/d3221401-785c-49ff-aa2d-e1bcf390f3c3/shutterstock_263091443,h_400,q_80,w_640.jpg)
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Sample needs to be representative
Sample needs to be representative
- When choosing a sample it is important for it to be representative of the whole population so that measurements we take in the sample can be used as estimates for the population.
- To be representative the sample needs to be big enough to be reliable, and the sample should be random so that every member of the population is equally likely to be chosen.
![Illustrative background for Random sample](https://image-v2.cdn.app.senecalearning.com/2018-03/fb787d2a-e14c-4891-83c2-45e6ab1229d7/shutterstock_112261553,h_400,q_80,w_640.jpg)
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Random sample
Random sample
- To choose a random sample you can assign a number to each member of the population then use a computer or a random number table or pick numbers out of a hat to choose a random selection of numbers.
- Pick the members corresponding to these numbers.
![Illustrative background for Biased sample](https://image-v2.cdn.app.senecalearning.com/2018-03/61fb3f58-510e-4731-8278-1e231312c7cd/shutterstock_539307937,h_400,q_80,w_640.jpg)
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Biased sample
Biased sample
- A biased sample is one that doesn’t represent the whole population.
- To assess whether a sample is biased think whether any groups of people would be excluded from the sample (e.g. based on gender, age, different interests or habits).
- A small sample is also likely to be biased.
Types of Data
Types of Data
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Primary vs secondary
Primary vs secondary
- Primary data is data that you have collected yourself.
- Data from any other source (e.g. from a book or the internet) is secondary data.
![Illustrative background for Qualitative vs quantitative](https://image-v2.cdn.app.senecalearning.com/2018-03/4f61f108-c184-4a88-b218-cd04dd2babfb/shutterstock_513941314,h_400,q_80,w_640.jpg)
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Qualitative vs quantitative
Qualitative vs quantitative
- Qualitative data is descriptive or categorical and uses words rather than numbers (e.g. colours, names).
- Quantitative data is measured in numbers and represents quantities (e.g. heights, shoe size).
![Illustrative background for Discrete vs continuous](https://image-v2.cdn.app.senecalearning.com/2018-03/42e264ef-adae-4303-8252-515134577806/shutterstock_740460751,h_400,q_80,w_640.jpg)
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Discrete vs continuous
Discrete vs continuous
- Quantitative data is discrete if the numbers can only take certain values (e.g. only whole numbers).
- It is continuous if the numbers can take any value.
Capture-Recapture Method
Capture-Recapture Method
A capture-recapture method can be used to estimate the population size from a sample.
![Illustrative background for Process](https://image-v2.cdn.app.senecalearning.com/2018-03/41b85c63-348a-4c1b-92dc-619b846fff0f/shutterstock_791125765,h_400,q_80,w_640.jpg)
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Process
Process
- A sample is captured, tagged and released.
- Later another sample is taken and the number of tagged members is noted.
- Using the assumption that the proportion of tagged members in the population is the same as the proportion in the sample you can then estimate the population.
![Illustrative background for Example](https://image-v2.cdn.app.senecalearning.com/2018-03/5199732f-77aa-4161-8d34-3966631a9be8/shutterstock_337861145,h_400,q_80,w_640.jpg)
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Example
Example
- A biologist captures 15 turtles from a lake and marks their shells with paint.
- The next week they capture 20 turtles and find 5 have their shells marked.
- 5⁄20 = 15⁄N where N is the population size so the estimate is N = 60.
1Number
1.1Using Numbers
1.1.1Equal Symbols
1.1.2Negative Numbers
1.1.3BIDMAS
1.1.4Inverse Operations
1.1.5End of Topic Test- Ordering
1.1.6Factors
1.1.7Multiples
1.1.8Highest Common Factor
1.1.9Lowest Common Multiple
1.1.10Number of Ways to Do a Task
1.1.11Number of Combinations
1.1.12Number of Ways To Arrange Objects
1.1.13End of Topic Test - Factors, Multiples & Combos
1.1.14Standard Form
1.1.15Ordinary Numbers to Standard Form
1.1.16Addition in Standard Form
1.1.17Subtraction in Standard Form
1.1.18Multiplication in Standard Form
1.1.19Division in Standard Form
1.1.20Exam-Style Questions - Standard Form & Primes
1.1.21Long Division
1.1.22Prime Numbers
1.1.23End of Topic Test - Standard Form & Long Division
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions
1.2.2Subtracting Fractions
1.2.3Multiplying Fractions
1.2.4Dividing Fractions
1.2.5Mixed Fractions
1.2.6Calculating Percentages of Numbers
1.2.7Calculating Fractions of Numbers
1.2.8Multiply Decimals
1.2.9Place Value
1.2.10Recurring Decimals
1.2.11Exam-Style Questions - Recurring Decimals
1.2.12Convert Fractions & Terminating Decimals
1.2.13Convert Recurring Decimals
1.2.14Convert Decimals & Percentages
1.2.15Compare Decimals
1.2.16Compare Fractions
1.2.17Exam-Style Questions - Percentages
1.2.18End of Topic Test - Fractions & Decimals
1.3Powers & Roots
1.3.1Powers
1.3.2Roots
1.3.3Indices Advanced
1.3.4Estimating Powers
1.3.5Estimating Roots
1.3.6Multiplying Powers
1.3.7Dividing Powers
1.3.8Power Raised to Power
1.3.9Fractions Raised to a Power
1.3.10Numbers Raised to Negative Powers
1.3.11Roots of Numbers
1.3.12Numbers to the Power of 1 & 0
1.3.13Surds
1.3.14Simplify Surds
1.3.15Rationalise Denominator
1.3.16Exam-Style Questions - Indices
1.3.17End of Topic Test - Powers & Roots
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics
2.1.2Substituting Values
2.1.3Algebraic Vocabulary
2.1.4Collecting Terms
2.1.5End of Topic Test - Algebra Basics & Power Rules
2.1.6Expanding Brackets I
2.1.7Common Factors
2.1.8Expanding Brackets II
2.1.9Rearrange For x
2.1.10Rearrange with Powers
2.1.11Exam-Style Questions - Basics of Algebra
2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations
2.8.2Linear Equations with Fractions
2.8.3Solve Linear Equations Graphically
2.8.4Quadratic ±
2.8.5Factorise Quadratics
2.8.6Quadratic Formula
2.8.7Complete the Square
2.8.8Solve Quadratics Graphically
2.8.9End of Topic Test - Solving Equations
2.8.10Simultaneous Equations
2.8.11Quadratic Simultaneous Equations
2.8.12Simultaneous Equations - Graphs
2.8.13Simultaneous Equations - Word Problems
2.8.14Approximate Solutions - Number of Iterations
2.8.15Approximate Solutions - Iterations to 1 DP
2.8.16Approximate Solutions - Iteration Formula
2.8.17Exam-Style Questions - Simultaneous Equations
2.8.18End of Topic Test - Simultaneous Equations
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules
2.10.2Recurrence Relationships
2.10.3Find Nth Term in Linear Sequence
2.10.4Check If a Number is In a Sequence
2.10.5Exam-Style Questions - Sequences
2.10.6Arithmetic & Geometric Progressions
2.10.7Key Sequences
2.10.8Quadratic Sequences
2.10.9Find Nth Term in Quadratic Sequence
2.10.10Exam-Style Questions - Geometric Series
2.10.11End of Topic Test - Sequences
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios
3.2.2Turn Ratios into Equations
3.2.3Ratio Notation & Reduction
3.2.4End of Topic Test - Units & Ratios
3.2.5Part : Part Ratio
3.2.6Part : Whole Ratio
3.2.7Two Ratios
3.2.8Differences in Ratios
3.2.9Fractions in Ratios
3.2.10Numbers as Fractions
3.2.11Ratios to Fractions
3.2.12Exam-Style Questions - Ratios
3.2.13End of Topic Test - Fractions & Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals
3.3.2Convert Percentages to Fractions
3.3.3Find the Percentage
3.3.4More/Less Percentage
3.3.5Price from Percentage Change
3.3.6Calculate Percentage Change from Price
3.3.7End of Topic Test - Percentages
3.3.8Profit & Interest & Discount
3.3.9Original Price after Discounts
3.3.10Simple Interest
3.3.11Compound Growth & Decay
3.3.12Compound Interest
3.3.13Compound Interest - After How Many Days?
3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics
4.1.2Geometry Basics 2
4.1.3Regular Polygons
4.1.4Triangles & Angles
4.1.5Midpoint
4.1.6Bisectors & Perpendiculars
4.1.7Locus
4.1.8Angle rules
4.1.9Parallel Angle Rules
4.1.10Angles in a Polygon
4.1.11Angles in a Triangle
4.1.12Exam-Style Questions - Angles in Shapes
4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape
4.9.2Plans & Elevations
4.9.3Nets
4.9.4Volume of 3D Shapes
4.9.5Volume of a Cuboid
4.9.6Volume of a Cylinder
4.9.7Volume of a Sphere
4.9.8Volume of a Hemisphere
4.9.9Volume of a Cone
4.9.10Volume of a Pyramid
4.9.11Surface Area & Composite Shapes
4.9.12Surface Area of a Cuboid
4.9.13Surface Area of a Cylinder
4.9.14Surface Area of a Sphere/Hemisphere
4.9.15Surface Area of a Cone
4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities
5.3.2Multiple Events
5.3.3Probability Calculations
5.3.4Dependent Events
5.3.5Independent Events
5.3.6Probability Tree Diagram
5.3.7Complex Tree Diagrams
5.3.8Conditional Probability
5.3.9Conditional Probability From a Two Way Table
5.3.10Conditional Probability Venn Diagrams
5.3.11Conditional Probability Tree Diagrams
5.3.12Exam-Style Questions - Probability
5.3.13End of Topic Test - Probability
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts
6.2.2Pie Charts
6.2.3Stem & Leaf Diagrams
6.2.4Back to Back Stem & Leaf Diagrams
6.2.5End of Topic Test - Statistics
6.2.6Pictograms
6.2.7Time Series Graphs
6.2.8Histograms
6.2.9Histograms 2
6.2.10Frequency Polygons
6.2.11Cumulative Frequency
6.2.12Cumulative Frequency 2
6.2.13Scatter Graphs
6.2.14Scatter Graphs - Predictions
6.2.15Correlation & Causation
6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
Jump to other topics
1Number
1.1Using Numbers
1.1.1Equal Symbols
1.1.2Negative Numbers
1.1.3BIDMAS
1.1.4Inverse Operations
1.1.5End of Topic Test- Ordering
1.1.6Factors
1.1.7Multiples
1.1.8Highest Common Factor
1.1.9Lowest Common Multiple
1.1.10Number of Ways to Do a Task
1.1.11Number of Combinations
1.1.12Number of Ways To Arrange Objects
1.1.13End of Topic Test - Factors, Multiples & Combos
1.1.14Standard Form
1.1.15Ordinary Numbers to Standard Form
1.1.16Addition in Standard Form
1.1.17Subtraction in Standard Form
1.1.18Multiplication in Standard Form
1.1.19Division in Standard Form
1.1.20Exam-Style Questions - Standard Form & Primes
1.1.21Long Division
1.1.22Prime Numbers
1.1.23End of Topic Test - Standard Form & Long Division
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions
1.2.2Subtracting Fractions
1.2.3Multiplying Fractions
1.2.4Dividing Fractions
1.2.5Mixed Fractions
1.2.6Calculating Percentages of Numbers
1.2.7Calculating Fractions of Numbers
1.2.8Multiply Decimals
1.2.9Place Value
1.2.10Recurring Decimals
1.2.11Exam-Style Questions - Recurring Decimals
1.2.12Convert Fractions & Terminating Decimals
1.2.13Convert Recurring Decimals
1.2.14Convert Decimals & Percentages
1.2.15Compare Decimals
1.2.16Compare Fractions
1.2.17Exam-Style Questions - Percentages
1.2.18End of Topic Test - Fractions & Decimals
1.3Powers & Roots
1.3.1Powers
1.3.2Roots
1.3.3Indices Advanced
1.3.4Estimating Powers
1.3.5Estimating Roots
1.3.6Multiplying Powers
1.3.7Dividing Powers
1.3.8Power Raised to Power
1.3.9Fractions Raised to a Power
1.3.10Numbers Raised to Negative Powers
1.3.11Roots of Numbers
1.3.12Numbers to the Power of 1 & 0
1.3.13Surds
1.3.14Simplify Surds
1.3.15Rationalise Denominator
1.3.16Exam-Style Questions - Indices
1.3.17End of Topic Test - Powers & Roots
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics
2.1.2Substituting Values
2.1.3Algebraic Vocabulary
2.1.4Collecting Terms
2.1.5End of Topic Test - Algebra Basics & Power Rules
2.1.6Expanding Brackets I
2.1.7Common Factors
2.1.8Expanding Brackets II
2.1.9Rearrange For x
2.1.10Rearrange with Powers
2.1.11Exam-Style Questions - Basics of Algebra
2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations
2.8.2Linear Equations with Fractions
2.8.3Solve Linear Equations Graphically
2.8.4Quadratic ±
2.8.5Factorise Quadratics
2.8.6Quadratic Formula
2.8.7Complete the Square
2.8.8Solve Quadratics Graphically
2.8.9End of Topic Test - Solving Equations
2.8.10Simultaneous Equations
2.8.11Quadratic Simultaneous Equations
2.8.12Simultaneous Equations - Graphs
2.8.13Simultaneous Equations - Word Problems
2.8.14Approximate Solutions - Number of Iterations
2.8.15Approximate Solutions - Iterations to 1 DP
2.8.16Approximate Solutions - Iteration Formula
2.8.17Exam-Style Questions - Simultaneous Equations
2.8.18End of Topic Test - Simultaneous Equations
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules
2.10.2Recurrence Relationships
2.10.3Find Nth Term in Linear Sequence
2.10.4Check If a Number is In a Sequence
2.10.5Exam-Style Questions - Sequences
2.10.6Arithmetic & Geometric Progressions
2.10.7Key Sequences
2.10.8Quadratic Sequences
2.10.9Find Nth Term in Quadratic Sequence
2.10.10Exam-Style Questions - Geometric Series
2.10.11End of Topic Test - Sequences
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios
3.2.2Turn Ratios into Equations
3.2.3Ratio Notation & Reduction
3.2.4End of Topic Test - Units & Ratios
3.2.5Part : Part Ratio
3.2.6Part : Whole Ratio
3.2.7Two Ratios
3.2.8Differences in Ratios
3.2.9Fractions in Ratios
3.2.10Numbers as Fractions
3.2.11Ratios to Fractions
3.2.12Exam-Style Questions - Ratios
3.2.13End of Topic Test - Fractions & Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals
3.3.2Convert Percentages to Fractions
3.3.3Find the Percentage
3.3.4More/Less Percentage
3.3.5Price from Percentage Change
3.3.6Calculate Percentage Change from Price
3.3.7End of Topic Test - Percentages
3.3.8Profit & Interest & Discount
3.3.9Original Price after Discounts
3.3.10Simple Interest
3.3.11Compound Growth & Decay
3.3.12Compound Interest
3.3.13Compound Interest - After How Many Days?
3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics
4.1.2Geometry Basics 2
4.1.3Regular Polygons
4.1.4Triangles & Angles
4.1.5Midpoint
4.1.6Bisectors & Perpendiculars
4.1.7Locus
4.1.8Angle rules
4.1.9Parallel Angle Rules
4.1.10Angles in a Polygon
4.1.11Angles in a Triangle
4.1.12Exam-Style Questions - Angles in Shapes
4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape
4.9.2Plans & Elevations
4.9.3Nets
4.9.4Volume of 3D Shapes
4.9.5Volume of a Cuboid
4.9.6Volume of a Cylinder
4.9.7Volume of a Sphere
4.9.8Volume of a Hemisphere
4.9.9Volume of a Cone
4.9.10Volume of a Pyramid
4.9.11Surface Area & Composite Shapes
4.9.12Surface Area of a Cuboid
4.9.13Surface Area of a Cylinder
4.9.14Surface Area of a Sphere/Hemisphere
4.9.15Surface Area of a Cone
4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities
5.3.2Multiple Events
5.3.3Probability Calculations
5.3.4Dependent Events
5.3.5Independent Events
5.3.6Probability Tree Diagram
5.3.7Complex Tree Diagrams
5.3.8Conditional Probability
5.3.9Conditional Probability From a Two Way Table
5.3.10Conditional Probability Venn Diagrams
5.3.11Conditional Probability Tree Diagrams
5.3.12Exam-Style Questions - Probability
5.3.13End of Topic Test - Probability
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts
6.2.2Pie Charts
6.2.3Stem & Leaf Diagrams
6.2.4Back to Back Stem & Leaf Diagrams
6.2.5End of Topic Test - Statistics
6.2.6Pictograms
6.2.7Time Series Graphs
6.2.8Histograms
6.2.9Histograms 2
6.2.10Frequency Polygons
6.2.11Cumulative Frequency
6.2.12Cumulative Frequency 2
6.2.13Scatter Graphs
6.2.14Scatter Graphs - Predictions
6.2.15Correlation & Causation
6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
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