Level 3 Statistics A
13STA Course DescriptionTeacher in Charge: Mr M. Po'e-Tofaeono.
Recommended Prior LearningMerit or better in AS91267 (Probability) and at least 12 credits in Level 2 Mathematics Combined or Mathematics with Calculus or Level 2 Statistics or at the discretion of the Teacher in Charge or Learning Area Director.
Choosing the Right Mathematics Course for You
At Level 2 and 3, Mathematics splits into more specialised courses. Your choice should reflect your learning strengths and future plans. Below is a guide to help you decide which pathway is best for you.
Statistics is the study of data, how it is collected, analysed, and interpreted to support decision-making. It enables us to identify patterns, assess reliability, and make informed predictions based on evidence. Students develop skills in evaluating real-world information and drawing conclusions using statistical techniques.
Statistics is widely applied in fields such as health sciences, psychology, law, business, education, and environmental studies.
Calculus is the branch of mathematics concerned with change and motion. It focuses on rates of change and the accumulation of quantities, using algebraic and graphical methods to model real-world situations. Students learn to solve complex problems involving speed, growth, area under curves, and optimisation.
Calculus is essential for careers in engineering, physics, architecture, computer science, and any discipline requiring advanced mathematical modelling.
LEVEL 3 STATISTICS A
Probability and statistics are used to solve problems, model situations, make predictions and analyse data. There is the opportunity to develop critical thinking skills in analysing and interpreting information and communicating the findings. There is a strong emphasis on the use of technology. A parallel course ( 13STB) which is primarily internally assessed is also available.
If you are unsure which course of Mathematics to study, speak to your current Maths teacher. They know your strengths and can help you decide which course best suits your goals.
Course Overview
Term 1
The following topics will be covered, however, due to unforeseen circumstances, topic order and concepts might change throughout the year.
BIVARIATE ANALYSIS
-Use the statistical enquiry cycle to plan, process, analyse and interpret data
-Identify the relationship between two numerical variables (e.g. height and arm span)
-Create and interpret scatter plots to visually assess patterns
-Use linear regression to model the relationship between two variables
-Interpret slope (gradient) and y-intercept in context
-Understand and comment on strength, direction, and form of the relationship
-Identify and discuss outliers and their possible effect
-Use correlation coefficient (r) and coefficient of determination (r²) to describe how well the line fits the data
-Make predictions using the regression line and identify whether they are interpolations (safe) or extrapolations (less reliable)
-Communicate findings with appropriate supporting evidence, context, and limitations
EVALUATE STATISTICALLY BASED REPORTS
-Critically read and evaluate a real-world statistical report (e.g. from a news article, research summary, government document)
-Identify the purpose of the report what question(s) is it trying to answer?
-Assess the population of interest and how the data was collected (e.g. survey, observational study, experiment)
-Evaluate whether the sample is representative of the population
-Consider the method of data collection were there possible sources of bias?
-Interpret the statistical measures used (e.g. percentages, medians, margins of error)
-Check whether language used in the report is appropriate does it overstate or mislead?
e.g. Does it wrongly claim causation from correlation?
-Identify and evaluate any assumptions or limitations in the report
-Determine whether the conclusions are justified based on the data and methods
-Clearly communicate your critique using evidence and statistical reasoning
Term 2
STATISTICAL INFERENCE
-Investigate a question comparing two groups or treatments (e.g. Do Year 12s sleep more than Year 13s?)
-Use the statistical enquiry cycle to:
*Pose a comparison question
*Plan and carry out a data collection method
*Analyse and interpret the results
*Use informal confidence intervals (like bootstrapping or resampling) to compare group medians or means
*Describe and interpret sampling variation how results might differ if a new sample were taken
*Use dot plots or difference graphs to compare distribution shapes, spread, and centres
-Make a formal inference by:
*Describing the observed difference
*Interpreting the confidence interval (e.g. "We are fairly sure the true difference in medians is between 2.1 and 4.3")
*Explaining whether the difference is likely due to chance or reflects a real effect
-Comment on the strength of evidence and practical significance
-Reflect on any limitations (e.g. small sample size, non-random sample) and how they affect the reliability of the conclusion
-Write clear, contextual conclusions that connect back to the original investigative question
PROBABILITY CONCEPTS
-Use probability rules:
-Complement rule:
-Addition rule for mutually exclusive events:
-General addition rule:
-Multiplication rule for independent events:
-Understand and apply conditional probability:
-Use two-way tables, Venn diagrams, and tree diagrams to model and calculate probabilities
-Identify whether events are independent or dependent, and mutually exclusive or not
-Use probability to solve real-world contextual problems
-Justify your answers using clear reasoning, notation, and interpretation in context
Term 3
PROBABILITY CONCEPTS continued
PROBABILITY DISTRIBUTIONS
-Identify and use discrete probability distributions (e.g. binomial, geometric)
-Calculate exact and cumulative probabilities using formulas or technology
-Use and interpret normal distributions (continuous probability)
-Standardise values using z-scores:
-Use z-tables or technology to find probabilities for ranges
-Understand the mean (μ) and standard deviation (σ) in context
-Estimate probabilities and expected values in real-world contexts (e.g. reliability testing, quality control, finance)
-Solve contextual problems using appropriate distribution models
-Communicate clearly, explaining your reasoning and interpreting results in context
-Optional student-friendly phrasing:
-Use maths to work out the chance of things happening from simple or complex situations"
-Apply rules and models to real-life situations like games, medical testing, or quality control"
-Understand how things vary, and how likely different outcomes are"
Term 4
Review all prior concepts in preparation for NCEA external examinations.
Course Costs and Equipment/ Stationery requirements
Students will need a Casio graphic calculator (fx-9860GIII, approximately $180). Older models such as the Casio fx-9750G are also suitable. If in doubt, please check with your Mathematics teacher before purchasing whether from the school or other retailers.
Year 13 Statistics Workbooks, $30.
Note: All prices are approximate and may change slightly due to updates from suppliers or production costs. We will do our best to keep any changes as minimal as possible.
If the cost of any item presents a challenge, we warmly encourage you to contact the Dean early in Term 1 next year to discuss possible support.