Statistics

  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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Investigating Data Distributions
Types of Data
Categorical Distributions
Numerical Distributions
​The Log (Base 10) Scale
​Summary of the Distribution of Numerical Variables
​The Normal Distribution (The 68-95-99.7% Rule)
Standardised Values (z-Scores)

​Investigating Associations Between Two Variables
Response and Explanatory Variables
​Associations between Categorical Variables
Associations between Numerical and Categorical Variables
Associations between Numerical Variable: Scatterplots
​Pearson's Product Moment Correlation Coefficient
Calculating the Correlation Coefficient Manually
Cause and Effect
​Non-Causal Explanations for Observered Associations

Investigating and Modelling Linear Associations
Determining the Least Squares Regression Line
​Sketching a Least Squares Regression Line
​Interpreting a Least Squares Regression Line
​Predicting with a Least Squares Regression Line
​Coefficient of Determination
​​Residual Analysis ​
Data Transformations
​Determining the Best Transformation
​Predicting with a Transformed Least Squares Regression Line

​Investigating and Modelling Time Series Data
​Time Series
​Numerical Smoothing - Moving Mean
Graphical Smoothing - Moving Median
​Seasonal Adjustment ​
Modelling Trends and Forecasting
​
Discrete Random Variables
Random Variables
Discrete Random Variables
Events from a Sample Space
Transitional Probabilities 
​Sampling without Replacement
Statistics of Discrete Random Variables
​Proof of Linear Combinations of Discrete Random Variables
Bernoulli Distribution
​Binomial Distribution
Statistics of Binomial Random Variables
Parameters of Binomial Distributions
​Discrete Random Variables Technology [TI-nSpire] 
Discrete Random Variables Technology ​[Casio]

Continuous Random Variables
​Continuous Random Variables
Statistics of Continuous Random Variables
​Proof of Linear Combinations of Continuous Random Variables
​Conditional Probability - Continuous Random Variables
Cumulative Density Functions 
Normal Distribution
Density Functions for the Normal Distribution 
Parameters of Normal Distributions
​Inverse Normal Distribution [TI-nSpire]
Inverse Normal Distribution ​[Casio]
Continuous Random Variable Technology [TI-nSpire]
Continuous Random Variable Technology ​[Casio]

Statistical Inference, including Definition and Distribution of Sample Proportions, Simulations, and Confidence Intervals
Statistical Inference
​Sample Distribution of Proportions
Statistics of Sample Distribution of Proportions
Normal Approximation for Sample Proportions
​Simulation of Random Sampling [TI-nSpire]
Simulation of Random Sampling [Casio]
​​​​Confidence Intervals for Proportions
Simulation of Variations in Confidence Intervals [TI-nSpire]
Simulation of Variations in Confidence Intervals [Casio]
​​Sample Proportion Technology [TI-nSpire]
Sample Proportion Technology ​[Casio]​​

Linear Combination of Random Variables
Linear Combination of Random Variables
Probabilities of Linear Combinations of Random Variables​

Sample Proportions
Statistical Inference
​Sample Distribution of Proportions
Statistics of Sample Distribution of Proportions
Normal Approximation for Sample Proportions

Sample Means
Sample Distribution of Means
Probabilities involving Sample Means
​Simulation to Illustrate Properties of X Bar [TI-nSpire]
Simulation to Illustrate Properties of X Bar [Casio]
Normal Approximation for Sample Means

Confidence Intervals
​​​​Confidence Intervals for Proportions
​Confidence Intervals for Means
​Simulation of Variations in Confidence Intervals [TI-nSpire]
Simulation of Variations in Confidence Intervals [Casio]
​
Hypothesis Testing
​Hypotheses and p-Values
​Hypothesis Testing
​Errors in Hypothesis Testing​​​
Probabilities of Probabilities
Essence of Probability
View of Challenging misconceptions about the coefficient of determination (R^2) with a dynamic Geogebra applet (Meagher, Edwards, Ozg ̈un-Koca Article and Interactive)
Binomial random sample with distribution graph (Desmos Interactive)

Crash Course Statistics
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer. 

Investigating Data Distributions
Types of Data (2016-2022 Study Design Questions)
Types of Data (2000-2015 Study Design Questions)
Categorical Data (2016-2022 Study Design Questions)
Categorical Data (2000-2015 Study Design Questions)
Numerical Data: Dot Plots, Stem Plots, and Histograms (2016-2022 Study Design Questions)
Numerical Data: Dot Plots, Stem Plots, and Histograms (2000-2015 Study Design Questions)
​Histograms using a Log (Base 10) Scale (2016-2022 Study Design Questions)
Numerical Data: Boxplots, Fences, and Outliers (2016-2022 Study Design Questions)
Numerical Data: Boxplots, Fences, and Outliers (2000-2015 Study Design Questions)
Numerical Data: Mean and Standard Deviation (2016-2022 Study Design Questions)
Numerical Data: Mean and Standard Deviation (2000-2015 Study Design Questions)
Normal Distribution (2016-2022 Study Design Questions)
Normal Distribution (2000-2015 Study Design Questions)

Investigating Associations Between Two Variables
Response and Explanatory Variables (2016-2022 Study Design Questions)
​Response and Explanatory Variables (2000-2015 Study Design Questions)
Association between Categorical Variables (2016-2022 Study Design Questions)
Associations between Categorical Variables (2000-2015 Study Design Questions)
​Association between Numerical and Categorical Variables ​(2016-2022 Study Design Questions)
​Association between Numerical and Categorical Variables (2000-2015 Design Questions)
Scatterplots: Association between Numerical Variables (2016-2022 Study Design Questions)
Scatterplots: Association between Numerical Variables (2000-2015 Study Design Questions)
​Correlation Coefficient (2016-2022 Study Design Questions)
Correlation Coefficient (2000-2015 Study Design Questions)
Correlation vs. Causation (2016-2022 Study Design Questions)
​Correlation vs. Causation (2000-2015 Study Design Questions)
Which Display? (2016-2022 Study Design Questions)
Which Display? (2000-2015 Study Design Questions)

​Investigating and Modelling Linear Associations
​Determine and Draw Least-Squares Lines (2016-2022 Study Design Questions)
Determine and Draw Least-Squares Lines (2000-2015 Study Design Questions)
​Using and Analysing the Least-Squares Line (2016-2022 Study Design Questions)
Using and Analysing the Least-Squares Line (2000-2015 Study Design Questions)
​Coefficient of Determination (2016-2022 Study Design Questions)
Coefficient of Determination (2000-2015 Study Design Questions)
​Residual Analysis (2016-2022 Study Design Questions)
Residual Analysis (2000-2015 Study Design Questions)
Transformations (2016-2022 Study Design Questions)
​Transformations (2000-2015 Study Design Questions)

Investigating and Modelling Time Series Data
​Features of a Time Series (2016-2022 Study Design Questions)
Features of a Time Series (2000-2015 Study Design Questions)
Smoothing (2016-2022 Study Design Questions)
Smoothing (2000-2015 Study Design Questions)
Seasonal Adjustment (2016-2022 Study Design Questions)
Seasonal Adjustment (2000-2015 Study Design Questions)
​Linear Trends and Forecasting (2016-2022 Study Design Questions)
​​Linear Trends and Forecasting (2000-2015 ​Study Design Questions)



​
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Mathematical Methods Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
​
Discrete Random Variables
​Discrete Random Variables (2016-2022 Study Design Questions)
​Discrete Random Variables (2000-2015 Study Design Questions)
Events from a Sample Space (2016-2022 Study Design Questions)
Events from a Sample Space (2000-2015 Study Design Questions)
Sampling without Replacement (2016-2022 Study Design Questions)
Sampling without Replacement (2000-2015 Study Design Questions)
​Discrete Random Variables: Statistics (2016-2022 Study Design Questions)
​Discrete Random Variables: Statistics (2000-2015 Study Design Questions)

​Binomial Random Variables (2016-2022 Study Design Questions)
​Binomial Random Variables (2000-2015 Study Design Questions)
​Binomial Random Variables: Statistics (2016-2022 Study Design Questions)
​Binomial Random Variables: Statistics (2000-2015 Study Design Questions)

Continuous Random Variables
Continuous Random Variables (2016-2022 Study Design Questions)
​Continuous Random Variables (2000-2015 Study Design Questions)
​Continuous Random Variables: Statistics (2016-2022 Study Design Questions)
​Continuous Random Variables: Statistics (2000-2015 Study Design Questions)

Normally Distributed Random Variables (2016-2022 Study Design Questions)
​Normally Distributed Random Variables (2000-2015 Study Design Questions)
​Normally Distributed Random Variables: Statistics (2016-2022 Study Design Questions)
​Normally Distributed Random Variables: Statistics (2000-2015 ​Study Design Questions)

​Statistical Inference, including Definition and Distribution of Sample Proportions, Simulations, and Confidence Intervals
​Sample Distribution of Proportions (2016-2022 Study Design Questions)
​Sample Distribution of Proportions: Statistics (2016-2022 Study Design Questions)
​Confidence Intervals for Sample Proportions (2016-2022 Study Design Questions)




Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

​Linear Combinations of Random Variables (2016-2022 Study Design Questions)
Sample Distribution of Means (2016-2022 Study Design Questions)
​Confidence Intervals (2016-2022 Study Design Questions)
Hypothesis Testing (2016-2022 Study Design Questions)