3.1 Bivarite Data Analysis (20hr)
The Statistical Investigation Process
- review the statistical investigation process: identify a problem; pose a statistical question; collect or obtain data; analyse data; interpret and communicate results
Identifying and describing assosciations between two categorical variables
- Construct two way frequency tables and determine the *assosciated row and column sums and Percentages
- Use an appropriately percentaged Frequency Table to identify patterns and sugges the presence of an assosciation
- Describe an ssosciation in terms of differences observed in percentages across categories in a systematic and concise manner, and interpret this in the context of the data.
Identifying and describing associations between two numerical variables
- Construct a scatterplot to identify patterns in the data suggesting the presence of an association
- Describe an association between two numerical variables in terms of direction (positive/negative)
- Calculate, using technology, and interpret the Correlation Coefficient (r),to quanity the strength of a linear association
Fitting a linear model to numerical data
- Identify Relationship Variables and Response Variables for primary and secondary data
- use a Scatterplot to identify the nature of the relationship between variables
- model a Linear Relationship by fitting a Least-Squares Regression Line to the data
- use a Residual Plot to assess the appropriateness of fitting a Linear Model to the data (Linear model explained in Residuals)
- Interpret the intercept and slope of the fitted line
- use the Coefficient Of Determination to assess the strength of a linear association in terms of the explained variation
- use the equation of a fitted line to make predictions
- distinguish between Interpolation and Extrapolation when using the fitted line to make predictions, recognising the potential Dangers of Extrapolation.
- write up the results of the above analysis in a systematic and concise manner
Association and Causation
- Recognise that an observed assosciation between two variables does not necessarily mean that there is a causal relationship between them.
- identify possible non-causal explanation for an assosciation, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner.
Test 1 - Response - Bivariate Data Analysis - (7%) - Term 1 Week 2
The data investigation process
- Implement the statistical investigation process to answer questions that involve identifying, analysing and describing associations between two categorical variables or between two numerical variables.
Investigation 1 - Bivariate Data Analysis (6%) - Term 1 Week 9**
3.2 Growth and decay in sequences (15 hours)
The Arithmetic Sequencess
- use Recursion to generate an arithmetic sequence
I would interpret this as a Recursive Arithmetic Sequence
- display the terms of an Arithmetic Sequences in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model Linear Growth or Decay and decay in discrete situations.
- Deduce a rule for the
term of a particular Arithmetic Sequences from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions. - use arithmetic sequences to model and analyse practical situations involving Linear Growth or Decay.
The Geometric Sequence
- use recursion to generate a Geometric Sequence
Again, I would interpret this as creating a Recursive Geometric Sequence
- display the terms of a geometric sequence in both tabular and graphical form and demonstrate that Geometric Sequences can be used to model exponential growth and decay in discrete situations
- deduce a rule for the
term of a particular Geometric Sequence from the pattern of the terms in the sequence, and use this rule to make predictions - use Geometric Sequences to model and analyse (numerically, or graphically only) practical problems involving Geometric growth and decay.
Sequences generated by First Order Linear Recurrence Relation
- use a general First Order Linear Recurrence Relation relation to generate the terms of a sequence and to display it in both tabular and graphical form
- generate a sequence defined by a First Order Linear Recurrence Relation that gives long term increasing, decreasing or steady-state solutions
- use First Order Linear Recurrence relations to model and analyse (numerically or graphically only) practical problems
**Test 2 - Growth & Decay in Sequences - (6%) - Term 1 Week 8
**Investigation 2 - Growth & Decay in Sequences - (7%) Term 1 Week 9
3.3 Graphs and networks (20 hours)
The definition of a graph and assosciated terminology
- Demonstrate the meanings of, and use, the terms: graph Edge, Vertex, Loop, degree of a vertex,subgraph, simple graph, complete graph, Bipartite Graphs, Directed graph (digraph), Arc, Weighted graph, and network.
- Identify practical situations that can be represented by a network, and construct such networks.
- Construct an Adjacency Matrix from a given graph or digraph and use the matrix to solve assosciated problems.
Planar Graphs
- Demonstrate the meanings of, and use, the terms: Planar Graph and Face.
- apply Euler’s formula,
to solve problems relating to Planar Graphs.
Paths and cycles
- Demonstrate the meanings of, and use, the terms: [Walk, Trail, Path, Closed walk, Closed trail, Cycle, Connected Graph, and Bridge.
- Investigate and solve practical problems to determine the shortest path between two vertices in a Weighted graph. (by trial and error methods only)
- Demonstrate the meanings of, and use, the terms: Eulerian Trail, Eulerian graph, semi-Euerlian trail, and the conditions for their existence, and use these concepts to investigate and solve practical problems.
- Demonstrate the meanings of, and use, the terms: Hamiltonian graph, and semi-Hamiltonian graph, and use these concepts to investigate and solv practical problems
**Test 3 - Graphs & Networks - (7%) - Term 2 Week 3
Exam - (15%) - Term 2 Week 5-6