By Revision Genie
Statistical Enquiry Cycle
Unit 1
Defining a Statistical Question
Formulating Hypotheses
Choosing Data Collection Methods
Primary vs Secondary Data
Acknowledging Data Sources
Constraints in Data Collection
Ethical and Confidentiality Issues
Planning Data Representation Strategies
Organizing and Processing Data
Using Technology to Process Data
Generating Statistical Diagrams
Understanding Outputs from Technology
Calculating Statistical Measures
Choosing Appropriate Statistical Measures
Analyzing Diagrams and Calculations
Interpreting Results in Context
Making Predictions from Data
Evaluating Reliability of Findings
Identifying Weaknesses in Approach
Suggesting Improvements to Methods
Refining Hypotheses Through Iteration
Communicating Statistical Findings
Tailoring Communication to Audience
Evaluating Statistical Work
Handling Missing or Incorrect Data
Cleaning Data for Analysis
Recognizing Sensitivity in Data Collection
Using Control Groups in Experiments
Mitigating Non-Response Issues
Addressing Unexpected Outcomes
Designing Data Collection Sheets
Avoiding Leading Questions
Open vs Closed Questions in Surveys
Piloting Questionnaires
Pre-Testing Experiments
Using Matched Pairs in Control Groups
Identifying Extraneous Variables
Understanding Iterative Processes in Statistics
Recognizing Bias in Data Collection
Using Random Response Techniques
Interpreting Statistical Conclusions
Applying Statistical Techniques to Real Data
Understanding Statistical Constraints
Importance of Time in Data Collection
Cost Considerations in Data Collection
Confidentiality in Statistical Data
Using Statistical Software Effectively
Avoiding Graphical Misrepresentation
Selecting Appropriate Graphical Formats
Recognizing Errors in Data Representation
Making Inferences from Data
Using Statistical Measures to Compare Data
Unit 2
Types of Data
Definition of Qualitative Data
Definition of Quantitative Data
Understanding Discrete Data
Understanding Continuous Data
Categorical Data Explained
Ordinal Data Explained
Raw Data Characteristics
Ungrouped Data Overview
Grouped Data Overview
Bivariate Data Explained
Multivariate Data Explained
Advantages of Grouping Data
Implications of Grouping Data
Class Width in Grouped Data
Explanatory Variables Explained
Response Variables Explained
Scatter Diagram Axes
Primary Data Definition
Secondary Data Definition
Advantages of Primary Data
Disadvantages of Primary Data
Advantages of Secondary Data
Disadvantages of Secondary Data
Reliability of Data Sources
Accuracy of Data Sources
Constraints in Accessing Data
Merging Data into Categories
Loss of Accuracy When Grouping
Comparing Qualitative and Quantitative Data
Identifying Variables in Hypotheses
Recognizing Sensitivity Issues in Data
Statistical Terminology for Data Types
Unit 3
Populations and Sampling
Definition of Population
Examples of Populations
Definition of Sample Frame
Definition of Sample
Identifying a Population
Choosing a Sample Frame
Judgement Sampling
Opportunity Sampling
Cluster Sampling
Quota Sampling
Risks of Bias in Sampling
Random Sampling Technique
Systematic Sampling Technique
Quota Sampling Technique
Advantages of Random Sampling
Disadvantages of Random Sampling
Advantages of Systematic Sampling
Disadvantages of Systematic Sampling
Advantages of Quota Sampling
Disadvantages of Quota Sampling
Physical Methods for Random Sampling
Electronic Methods for Random Sampling
Ensuring Equal Likelihood in Sampling
Handling Repeated Random Numbers
Handling Out-of-Range Random Numbers
Definition of Stratification
Identifying Strata in a Population
Stratified Sampling Technique
Calculating Strata Sizes
Stratifying by Multiple Categories
Sources of Bias in Data Collection
Minimizing Bias in Sampling
Impact of Sample Size on Reliability
Reliability of Sampling Techniques
Understanding Non-Response Issues
Mitigating Sampling Challenges
Avoiding Coincidence in Systematic Sampling
Control Groups in Sampling
Matched Pairs in Control Groups
Cleaning Data Before Sampling
Extraneous Variables in Sampling
Impact of Population Size on Sampling
Use of Capture-Recapture Method
Assumptions in Capture-Recapture
Calculating Population Size Using Capture-Recapture
Common Biases in Sampling
Designing Sampling Techniques to Avoid Bias
Exam Trap: Misinterpreting Population Definitions
Exam Trap: Misusing Sampling Techniques
Exam Trap: Ignoring Bias in Sampling
Worked Example: Stratified Sampling Calculation
Worked Example: Random Sampling Procedure
Unit 4
Data Collection Methods
Definition of Primary Data
Definition of Secondary Data
Ethical Issues in Data Collection
Confidentiality in Data Collection
Time and Cost Constraints in Data Collection
Designing a Questionnaire
Open Questions in Questionnaires
Closed Questions in Questionnaires
Pilot Testing a Questionnaire
Minimizing Bias in Questionnaires
Observation as a Data Collection Method
Census as a Data Collection Method
Sampling as a Data Collection Method
Experimental Data Collection Methods
Simulations for Data Collection
Acknowledging Secondary Data Sources
Cleaning Data Before Processing
Handling Missing Data
Dealing with Non-Responses
Using Control Groups in Data Collection
Matched Pairs Technique in Experiments
Recording Data Effectively
Common Errors in Data Collection
Proactive Strategies for Mitigating Issues
Recognizing Sensitivity in Data Topics
Importance of Validity in Data Collection
Importance of Reliability in Data Collection
Examining Bias in Data Collection Methods
Choosing Between Primary and Secondary Data
Examples of Primary Data Sources
Examples of Secondary Data Sources
Impact of Data Rounding on Accuracy
Constraints in Accessing Secondary Data
Implications of Merging Data Categories
Grouping Numerical Data into Class Intervals
Loss of Accuracy in Grouped Data
Exam Trap: Misleading Questionnaire Design
Unit 5
Tabulation and Representation
Understanding Tabulation
Constructing Tally Charts
Interpreting Tally Charts
Introduction to Pie Charts
Drawing Pie Charts Using Angles
Interpreting Pie Charts
Comparative Pie Charts
Bar Charts Basics
Drawing Bar Charts
Interpreting Bar Charts
Composite Bar Charts
Histograms with Equal Class Widths
Frequency Density in Histograms
Drawing Histograms with Unequal Class Widths
Interpreting Histograms
Frequency Polygons Construction
Comparing Frequency Polygons
Cumulative Frequency Graphs Basics
Drawing Cumulative Frequency Graphs
Interpreting Cumulative Frequency Graphs
Box Plots Construction
Interpreting Box Plots
Stem and Leaf Diagrams Basics
Ordered Stem and Leaf Diagrams
Interpreting Stem and Leaf Diagrams
Two-Way Tables Basics
Using Two-Way Tables for Data Representation
Venn Diagrams Basics
Interpreting Venn Diagrams
Population Pyramids Interpretation
Choropleth Maps Basics
Using Choropleth Maps for Data Comparison
Identifying Graphical Misrepresentation
Errors in Graphical Scales
Distortion in 3D Representations
Choosing Appropriate Graphical Methods
Skewness from Data by Inspection
Interpreting Data Skewness
Presenting Data in Multiple Formats
Using Statistical Software for Visualization
Avoiding Misuse of Statistical Software
Comparing Data Sets Graphically
Unit 6
Measures of Central Tendency
Definition of Mean, Median, Mode
Understanding Arithmetic Mean
Calculating the Mean for Discrete Data
Calculating the Mean for Grouped Data
Using Class Midpoints to Estimate Mean
Effect of Adding Data on Mean
Effect of Scaling and Translation on Mean
Understanding the Median
Calculating the Median for Discrete Data
Calculating the Median for Grouped Data
Using Linear Interpolation for Median
Effect of Adding Data on Median
Effect of Scaling and Translation on Median
Understanding the Mode
Calculating the Mode for Discrete Data
Calculating the Modal Class for Grouped Data
Effect of Adding Data on Mode
Effect of Scaling and Translation on Mode
Choosing the Most Appropriate Measure of Central Tendency
Comparing Mean, Median, and Mode
Understanding Weighted Averages
Calculating Weighted Averages
Application of Weighted Averages in Context
Common Errors in Mean Calculations
Common Errors in Median Calculations
Common Errors in Mode Calculations
Interpreting Mean in Context
Interpreting Median in Context
Interpreting Mode in Context
Exam Trap: Misinterpreting Central Tendency in Skewed Data
Exam Trap: Miscalculating Grouped Data Mean
Exam Trap: Misidentifying Modal Class
Worked Example: Mean for Discrete Data
Worked Example: Mean for Grouped Data
Worked Example: Median for Discrete Data
Worked Example: Median for Grouped Data
Worked Example: Modal Class for Grouped Data
Worked Example: Weighted Averages in Real-World Context
Unit 7
Measures of Dispersion
Definition of Range
Calculating the Range
Definition of Quartiles
Finding Quartiles in Data Sets
Definition of Interquartile Range (IQR)
Calculating the Interquartile Range
Understanding Percentiles
Calculating Percentiles
Definition of Standard Deviation
Formula for Standard Deviation
Calculating Standard Deviation for Raw Data
Calculating Standard Deviation for Grouped Data
Understanding Variance
Relationship Between Variance and Standard Deviation
Definition of Outliers
Identifying Outliers by Inspection
Calculating Outlier Boundaries Using IQR
Calculating Outlier Boundaries Using Standard Deviation
Interpreting Outliers in Context
Comparing Data Sets Using Range
Comparing Data Sets Using IQR
Comparing Data Sets Using Percentiles
Comparing Data Sets Using Standard Deviation
Choosing Appropriate Measures of Dispersion
Pairing Measures of Central Tendency and Dispersion
Exam Trap: Misinterpreting Range
Exam Trap: Misinterpreting Quartiles
Exam Trap: Misinterpreting Standard Deviation
Using Technology to Calculate Dispersion Measures
Visualising Dispersion with Box Plots
Common Errors in Box Plot Construction
Understanding Interpercentile and Interdecile Ranges
Calculating Interpercentile Range
Calculating Interdecile Range
Using Dispersion Measures in Real-World Contexts
Exam Trap: Confusing Dispersion Measures
Standardised Scores and Dispersion
Formula for Standardised Scores
Calculating Standardised Scores
Using Standardised Scores to Compare Data Sets
Exam Trap: Misusing Standardised Scores
Unit 8
Scatter Diagrams and Correlation
What is a Scatter Diagram?
Plotting Points on a Scatter Diagram
Identifying Patterns in Scatter Diagrams
Explanatory and Response Variables
Positive Correlation in Scatter Diagrams
Negative Correlation in Scatter Diagrams
Zero Correlation in Scatter Diagrams
Strong and Weak Correlation
Correlation vs Causation
Examples of Spurious Correlation
Interpolation in Scatter Diagrams
Extrapolation in Scatter Diagrams
Risks of Extrapolation
Drawing a Line of Best Fit by Eye
Double Mean Point for Line of Best Fit
Using the Gradient of a Line of Best Fit
Using the Intercept of a Line of Best Fit
Making Predictions from Scatter Diagrams
Spearman’s Rank Correlation Coefficient
Interpreting Spearman’s Rank Correlation
Pearson’s Product Moment Correlation Coefficient
Interpreting Pearson’s Correlation Coefficient
Spearman vs Pearson Correlation
Common Errors in Scatter Diagrams
Examining Outliers in Scatter Diagrams
Choosing the Right Axis for Variables
Using Scatter Diagrams in Real-Life Contexts
Misrepresentation in Scatter Diagrams
Exam Tips for Scatter Diagrams
Unit 9
Time Series Analysis
Understanding Time Series Data
Identifying Trends in Data
Introduction to Moving Averages
Calculating 4-Point Moving Averages
Calculating Other Point Moving Averages
Plotting Moving Averages on a Graph
Drawing Trend Lines by Eye
Using Moving Averages to Draw Trend Lines
Interpreting the Gradient of Trend Lines
Identifying Seasonal Variations in Data
Understanding Cyclic Trends in Time Series
Calculating Average Seasonal Variation
Using Seasonal Variations to Make Predictions
Extrapolation and Its Risks in Time Series
Interpreting Time Series Graphs
Selecting Appropriate Time Series Analysis Methods
Common Mistakes in Time Series Analysis
Recognizing Patterns in Time Series Data
Exploring Real-World Applications of Time Series
Using Technology for Time Series Analysis
Evaluating Predictions in Time Series
Comparing Time Series Data Sets
Understanding the Statistical Enquiry Cycle in Time Series
Formulating Hypotheses for Time Series Analysis
Assessing Reliability of Time Series Predictions
Communicating Findings from Time Series Analysis
Unit 10
Probability Basics
Understanding Probability Scales
Using Likelihood Terms (e.g., Certain, Unlikely)
Experimental Probability Definition
Calculating Experimental Probability
Theoretical Probability Definition
Calculating Theoretical Probability
Comparing Experimental and Theoretical Probability
Relative Frequency and Probability
Estimating Probabilities from Frequency Tables
Estimating Probabilities from Relative Frequency Diagrams
Expected Frequency Definition
Calculating Expected Frequency from Probability
Interpreting Expected Frequency in Context
Probability as a Proportion
Probability on a 0-1 Scale
Probability on a 0-100% Scale
Absolute Risk Definition
Calculating Absolute Risk
Relative Risk Definition
Calculating Relative Risk
Interpreting Risks in Real-World Contexts
Experimental Probability and Bias
Identifying Bias in Experimental Design
Understanding Random Variables in Probability Experiments
Impact of Sample Size on Probability Estimates
Mutually Exclusive Events Definition
Exhaustive Events Definition
Addition Law for Mutually Exclusive Events
Addition Law for General Events
Independent Events Definition
Multiplication Law for Independent Events
Conditional Probability Definition
Calculating Conditional Probability
Experimental Probability and Theoretical Trends
Unit 11
Probability Representations
Introduction to Venn Diagrams
Union and Intersection in Venn Diagrams
Complement and Subset in Venn Diagrams
Mutually Exclusive Events in Venn Diagrams
Exhaustive Events in Venn Diagrams
Addition Rule Using Venn Diagrams
Worked Example: Venn Diagram Probability
Introduction to Tree Diagrams
Independent Events in Tree Diagrams
Conditional Probability in Tree Diagrams
Multiplication Rule Using Tree Diagrams
Worked Example: Tree Diagram Probability
Introduction to Sample Space Diagrams
Listing Outcomes in Sample Space Diagrams
Tabulating Outcomes in Sample Space Diagrams
Mutually Exclusive Events in Sample Space Diagrams
Exhaustive Events in Sample Space Diagrams
Addition Rule Using Sample Space Diagrams
Worked Example: Sample Space Diagram Probability
Comparing Venn, Tree, and Sample Space Diagrams
Choosing the Right Probability Representation
Common Errors in Venn Diagram Calculations
Common Errors in Tree Diagram Calculations
Common Errors in Sample Space Diagram Calculations
Interpreting Venn Diagrams for Probability
Interpreting Tree Diagrams for Probability
Interpreting Sample Space Diagrams for Probability
Using Venn Diagrams for Conditional Probability
Using Tree Diagrams for Conditional Probability
Using Sample Space Diagrams for Conditional Probability
Real-Life Applications of Venn Diagrams
Real-Life Applications of Tree Diagrams
Real-Life Applications of Sample Space Diagrams
Exam Tips for Venn Diagrams
Exam Tips for Tree Diagrams
Exam Tips for Sample Space Diagrams
Interpreting Complex Venn Diagrams
Constructing Accurate Tree Diagrams
Constructing Sample Space Diagrams Step-by-Step
Using Probability Representations in Multi-Step Problems
Understanding Overlapping Events in Venn Diagrams
Using Real Data in Probability Representations
Simplifying Complex Tree Diagrams
Visualizing Probability with Sample Space Diagrams
Connecting Probability Representations to Probability Rules
Critiquing Probability Representations for Accuracy
Matching Representations to Problem Contexts
Using Venn Diagrams for Absolute Risk Calculations
Using Tree Diagrams for Relative Frequency Calculations
Using Sample Space Diagrams for Expected Frequencies
Unit 12
Advanced Probability Concepts
Definition of Independent Events
Understanding Conditional Probability
Formal Notation for Conditional Probability
General Addition Law for Events
Using Two-Way Tables for Probability
Constructing Sample Space Diagrams
Tree Diagrams for Probability
Venn Diagrams for Probability
Mutually Exclusive and Exhaustive Events
Experimental Probability vs Theoretical Probability
Relative Frequency and Probability Estimates
Expected Frequency Calculations
Absolute Risk and Relative Risk
Identifying Bias in Experimental Probability
Characteristics of Binomial Distribution
Mean of Binomial Distribution
Conditions for Binomial Model Suitability
Calculating Binomial Probabilities
Characteristics of Normal Distribution
Symmetry and Bell Shape of Normal Distribution
Properties of Normal Distribution
Standard Deviations in Normal Distribution
Conditions for Normal Model Suitability
Unit 13
Index Numbers and Rates of Change
Understanding Index Numbers
Calculating Simple Index Numbers
Interpreting Index Numbers in Context
Weighted Index Numbers
Chain-Based Index Numbers
Retail Price Index (RPI)
Consumer Price Index (CPI)
Gross Domestic Product (GDP) Index
Common Misinterpretations of Index Numbers
Using Index Numbers for Comparisons
Rates of Change Formulae
Percentage Change Calculation
Interpreting Percentage Change in Context
Crude Birth Rate Formula
Standardised Birth Rate Formula
Making Predictions Using Rates of Change
House Prices and Rates of Change
Unemployment Rates Over Time
Graphical Representation of Rates of Change
Exam Trap: Misreading Index Numbers
Exam Trap: Misinterpreting Rates of Change
Worked Example: Calculating RPI
Worked Example: Calculating CPI
Worked Example: Using Birth Rate Formula
Worked Example: Interpreting House Price Trends
Worked Example: Predicting Unemployment Trends
Advantages of Using Index Numbers
Limitations of Index Numbers
Real-World Applications of Index Numbers
Real-World Applications of Rates of Change
Exam Technique: Index Numbers Questions
Exam Technique: Rates of Change Questions
Unit 14
Quality Assurance Techniques
Introduction to Quality Assurance
Purpose of Quality Assurance Techniques
Understanding Control Charts
Components of Control Charts
Action Lines in Control Charts
Warning Lines in Control Charts
Interpreting Control Charts
Sample Means in Quality Assurance
Using Medians in Quality Assurance Sampling
Using Ranges in Quality Assurance Sampling
Standard Deviations in Control Charts
Calculating Warning Limits
Calculating Action Limits
Steps for Constructing a Control Chart
Applications of Control Charts in Manufacturing
Applications of Control Charts in Service Industries
Common Errors in Control Chart Construction
Actions When Data Falls Outside Warning Limits
Actions When Data Falls Outside Action Limits
Statistical Methods for Process Monitoring
Sampling Techniques for Quality Assurance
Importance of Large Sample Sizes
Reliability and Validity in Quality Assurance
Minimizing Bias in Quality Assurance Applications
Using Technology in Quality Assurance
Real-Life Examples of Quality Assurance
Evaluating Quality Assurance Results
Improving Processes Based on Control Charts
Limitations of Control Charts
Using Statistical Software for Quality Assurance
Comparing Control Charts to Other Techniques
Examining Trends in Control Chart Data
Understanding Variation in Processes
Detecting Patterns in Quality Assurance Data
The Role of Standard Deviations in Process Control
Historical Development of Control Charts
Common Misinterpretations of Control Chart Data
Using Control Charts for Predictive Analysis
Statistical Assumptions in Control Charts
Real-Life Case Studies of Quality Assurance
Exam Tips for Quality Assurance Techniques
Unit 15
Estimation Methods
Purpose of Estimation in Statistics
Using Sample Data for Population Estimates
Population Mean Estimation from Samples
Predicting Population Proportions with Samples
Replication and Reliability in Sampling
Introduction to Capture-Recapture Method
Petersen Capture-Recapture Formula
Assumptions of Capture-Recapture Method
Appropriateness of Capture-Recapture Assumptions
Worked Example: Estimating Population Size
Common Errors in Capture-Recapture Calculations
Impact of Marking and Recapture Accuracy
Bias in Population Estimates
Comparing Estimation Methods
Limitations of Estimation Techniques
Examining Random Sampling in Estimation
Using Stratified Sampling for Estimation
Evaluating Representativeness of Samples
Confidence Intervals in Population Estimates
Factors Affecting Population Estimates
Worked Example: Sample Size and Reliability
Exam Trap: Misinterpreting Sample Data
Exam Trap: Incorrect Assumptions in Capture-Recapture
Worked Example: Capture-Recapture in Practice
Real-World Applications of Estimation Methods
Ethical Considerations in Population Sampling
Using Technology in Estimation Calculations
Calculating Estimates with Relative Frequency
Understanding Variability in Population Estimates
Interpreting Statistical Estimates in Context
Impact of Outliers on Population Estimation
Comparing Experimental and Theoretical Estimates
Using Graphs to Represent Population Estimates
Exam Trap: Misleading Graphical Representations
Worked Example: Comparing Two Population Estimates
Evaluating the Accuracy of Statistical Models
Exam Trap: Misusing Estimation Techniques
Strategies to Improve Estimation Accuracy
Using Historical Data for Population Estimates
Role of Statistical Software in Estimation
Worked Example: Estimation Using Stratified Sampling
Exam Trap: Overgeneralizing from Small Samples
Using Proportions to Estimate Population Characteristics
Understanding Sampling Error in Estimation
Worked Example: Estimation with Grouped Data
Exam Trap: Confusing Population and Sample Data
Comparing Capture-Recapture with Other Methods
Exam Trap: Miscalculating Capture-Recapture Results
Worked Example: Estimation Using Technology
Evaluating Statistical Assumptions in Estimation
Unit 16
Misuse and Bias in Statistics
Definition of Statistical Bias
Types of Statistical Bias
Selection Bias Explained
Non-Response Bias
Measurement Bias
Sampling Bias in Statistics
Response Bias in Surveys
Confirmation Bias in Data Analysis
Impact of Bias on Statistical Conclusions
Examples of Statistical Misuse
Misrepresentation of Data in Graphs
Misuse of Averages in Statistics
Cherry-Picking Data in Reports
The Role of Sample Size in Bias
How to Identify Bias in Data Collection
Strategies to Minimize Bias in Sampling
The Importance of Random Sampling
Issues with Non-Random Sampling Methods
Ethical Considerations in Data Collection
The Influence of Question Wording
Leading Questions in Surveys
Pilot Testing to Reduce Bias
Biased Sources in Secondary Data
Misleading Scales in Graphs
Truncated Axes in Data Representation
Misuse of 3D Graphs
Distorted Sizing in Graphs
Misinterpretation of Correlation and Causation
Spurious Correlation in Statistics
Interpolation vs Extrapolation Errors
Overgeneralization in Statistical Conclusions
Misuse of Percentages in Data Analysis
Misuse of Relative and Absolute Risks
Data Cleaning to Remove Bias
Impact of Outliers on Conclusions
Identifying Outliers in Data Sets
Examining Anomalies in Data
Misleading Visual Representations of Data
The Role of Context in Statistical Analysis
Misinterpretation of Statistical Terminology
Common Errors in Statistical Analysis
Evaluating the Reliability of Statistical Findings
Assessing the Validity of Statistical Methods
The Role of Peer Review in Statistics
How to Communicate Statistical Findings Clearly
Examining Real-World Examples of Statistical Misuse
Strategies to Avoid Misuse in Statistics
Exam Traps in Misuse and Bias Questions