STAT1008 Quantitative Research Methods
The Complete Exam Bible · S2 2026STAT1008 Overview
- 6 units
- S2 2026
- Level 1
- In person
- Two-hour final exam
STAT1008 Quantitative Research Methods is the Australian National University’s first-year course in gathering, describing and analysing quantitative information.
- Assessment Three in-semester quizzes and a group presentation precede a final exam worth 65%.
- Exam format An in-person two-hour paper on the whole syllabus, with a calculator provided.
- Hardest step Keeping probability, distributions and inference linked, since each builds on the last.
- How to prepare Work every example by hand to four decimals, then confirm it in Excel.
How STAT1008 is assessed
| Component | Weight | Format |
|---|---|---|
| Online Quiz | 5% | Week 4; redeemable; no extensions; open book |
| In-tutorial Probability Quiz | 5% | Week 5; written, closed book, 20 minutes, pen and calculator; non-redeemable |
| In-tutorial Canvas Quiz | 10% | Week 6; closed book; Excel data analysis on the lab computer; non-redeemable |
| In-tutorial Group Presentation | 15% | Weeks 9 to 12; teams of three to four; 12 to 15 minutes; non-redeemable |
| Final Exam | 65% | Final exam period; in person; 2 hours; whole syllabus; compulsory |
Weights, weeks and formats are those listed on the Semester 2, 2026 course information page and the first tutorial’s assessment slide. Confirm dates, rooms and any changes on Canvas.
Current STAT1008 dates
| Date | Item | Control |
|---|---|---|
| Weeks 9 to 12 | In-tutorial Group Presentation | Tutors randomly allocate each group to one of Weeks 9 to 12, and the group presents in its own computer lab time that week. |
| 30 October 2026 | Class end date | Teaching for the Second Semester 2026 class ends on this date. |
| Final exam period | Final Exam | The in-person final exam is worth 65% and covers the whole syllabus; check the personal exam timetable. |
Dates are as published in the Semester 2, 2026 course information and the ANU Programs and Courses class listing. Confirm exact deadlines and submission settings in the live LMS.
What STAT1008 covers
Eleven chapters follow the course schedule from data collection and summaries through probability and distributions to sampling distributions and confidence intervals.
Populations, Samples and Data Collection
Population and sample, parameter and statistic, sampling frames, random and non-random designs, variable types and survey errorPopulations, Samples and Data Collection sets up the vocabulary every later answer depends on.
- The statistical workflow from problem to decision
- Population, sample, parameter and statistic
- Exploratory analysis versus statistical inference
- Sampling frames and coverage
- Random and non-random sampling designs
- Categorical and numerical variable types
Tables and Charts for Summarising Data
Summary and contingency tables, row and column percentages, bar charts, frequency tables, histograms and scatter plotsTables and Charts for Summarising Data matches each display to the kind of data being summarised.
- Summary tables and bar charts
- Contingency tables with row, column and total percentages
- Side-by-side bar charts
- Frequency tables and class width
- Histograms and their shape
- Scatter plots and how to describe them
Measures of Centre, Variation and Shape
Mean, median and mode, variance and standard deviation, z-scores, skewness, the empirical rule, covariance and correlationMeasures of Centre, Variation and Shape turns data into numbers that can be compared.
- Mean, median and mode
- Resistant and non-resistant measures
- Variance and standard deviation
- Z-scores and outliers
- Skewness and the position of mean and median
- The empirical rule and Chebyshev
Quartiles, Boxplots and Outliers
The percentile location rule, quartiles and IQR, five-number summary, boxplot fences and two outlier rulesQuartiles, Boxplots and Outliers covers the course’s hand rule for percentiles, where the location index is P/100 times n, averaged when whole and rounded up when fractional.
- Percentiles and the location index
- Quartiles and the interquartile range
- The five-number summary
- Boxplot construction and fences
- Two outlier rules that can disagree
- Comparing groups with boxplots
Probability Rules and Contingency Tables
Events and sample spaces, union and intersection, addition and complement rules, conditional probability and independenceProbability Rules and Contingency Tables introduces random experiments, sample spaces and events, and the three sources of probability: a priori, empirical and subjective.
- Random experiments, sample spaces and events
- Three ways to assign a probability
- Union, intersection and complement
- Mutually exclusive and collectively exhaustive events
- Probabilities from a contingency table
- The general addition rule
Conditional Probability, Bayes and Counting
Probability trees, the multiplication and marginal rules, Bayes' theorem, permutations and combinationsConditional Probability, Bayes and Counting develops the general multiplication rule, the marginal probability rule written through conditionals, and probability trees that multiply along paths and add across them.
- The general multiplication rule
- Probability trees
- The marginal probability rule through conditionals
- Bayes’ theorem
- Factorials and the multiplication rule for counting
- Permutations and combinations
Discrete Random Variables and Expected Value
Valid probability distributions, expected value, variance and standard deviation, rules for transformed and summed variablesDiscrete Random Variables and Expected Value defines a random variable as a number attached to the outcome of a random experiment and a discrete distribution as a list of values with probabilities summing to 1. It computes the expected value as a probability-weighted average, the variance through E(X squared) minus the squared mean, and the standard deviation, then applies the rules for linear transformations and sums of independent variables.
- Random variables, discrete and continuous
- Requirements for a valid distribution
- Expected value as a long-run average
- Variance and standard deviation of a random variable
- Linear transformations aX + b
- Sums of independent random variables
The Binomial Distribution
The binomial conditions, exact and cumulative probabilities, BINOM.DIST, mean np and variance np(1 - p), solving for nThe Binomial Distribution models the number of successes in n independent trials with a constant success probability p.
- The four binomial properties
- The binomial formula and combinations
- At least and at most with the complement
- Cumulative probabilities and BINOM.DIST
- Mean and standard deviation of a binomial
- Solving for the number of trials
Normal and Uniform Distributions
Density curves, standardising to Z, forward and inverse normal problems, normality checks, the uniform model and the binomial approximationNormal and Uniform Distributions moves from tables to densities, where probability is area and any single value has probability zero.
- Density curves and probability as area
- Properties of the normal distribution
- Standardising to Z and the cumulative table
- Inverse normal problems
- Assessing normality
- The uniform distribution
Sampling Distributions and the Central Limit Theorem
The sampling distribution of the mean, standard error, the Central Limit Theorem and the sample proportionSampling Distributions and the Central Limit Theorem treats a statistic as a random variable whose value changes from sample to sample. The sample mean is unbiased for the population mean, with standard error sigma over the square root of n.
- Repeated sampling and the sampling distribution
- Unbiasedness of the sample mean
- Standard error and sample size
- Sampling from a normal population
- The Central Limit Theorem
- Sampling distribution of a proportion
Confidence Intervals for Means and Proportions
Point and interval estimates, z and t intervals for a mean, intervals for a proportion and sample-size planningConfidence Intervals for Means and Proportions builds intervals of the form point estimate plus or minus margin of error.
- Point and interval estimates
- Bias, sampling error and efficiency
- The z-interval for a mean
- Student’s t and degrees of freedom
- The interval for a proportion
- Interpreting a confidence interval
It treats statistics as the science of learning from data in order to make decisions under uncertainty, and it follows one chain throughout: a real problem, data collection, cleaning, exploration, modelling, conclusions and a better decision. It is taught each week through a pre-recorded lecture, a two-hour workshop and a one-hour computer-lab tutorial.
The first weeks are descriptive.
Students learn to define populations and samples, choose between simple random, stratified, systematic and cluster designs, recognise coverage, non-response and measurement error, and classify variables.
Data are then organised into summary and contingency tables, bar charts, histograms and scatter plots, and summarised with means, medians, standard deviations, quartiles, boxplots, z-scores, skewness and correlation.
The middle weeks build probability: events and contingency tables, counting rules, conditional probability, independence and Bayes’ theorem, followed by discrete random variables, the binomial distribution, the normal and uniform distributions and the normal approximation to the binomial.
The course then turns to inference, with sampling distributions, the Central Limit Theorem and confidence intervals, before continuing to hypothesis tests, regression, ANOVA and chi-squared tests. Microsoft Excel with the Analysis ToolPak is used for computing throughout, while the final exam relies on a provided calculator and hand working.
This guide follows that order chapter by chapter.
Each chapter explains a method, works an original example in full, shows a figure drawn from the example’s own numbers, and closes with practice questions and answers.
Worked example · free
Normal probability for battery life
- 1Standardise: z = (560 − 500)/40 = 1.50.
- 2From the cumulative table P(Z < 1.50) = 0.9332, so P(X > 560) = 1 − 0.9332 = 0.0668.
- 1Top 10%: the lower-tail area is 0.90, so z ≈ 1.28.
- 2Cut-off: x = 500 + 1.28 × 40 = 551.2 hours.
Key terms
- Population
- A population is every unit about which a conclusion is to be drawn.
- Sample statistic
- A sample statistic is a number calculated from sample data and used to estimate a population parameter.
- Simple random sampling
- Simple random sampling gives every unit in the frame an equal chance of selection.
- Coverage error
- Coverage error occurs when some groups in the population are missing from the sampling frame.
- Ordinal variable
- An ordinal variable is a categorical variable whose labels have a natural order.
- Sample variance
- The sample variance adds the squared distances of the observations from their mean and divides the total by n minus 1.
- Empirical rule
- The empirical rule states that about 68%, 95% and 99.7% of bell-shaped data lie within one, two and three standard deviations of the mean.
- Marginal probability
- A marginal probability is the probability of a single event without reference to any other event.
- Bayes’ theorem
- Bayes’ theorem gives the probability of a cause given observed evidence from the probabilities of the evidence under each cause.
- Binomial random variable
- A binomial random variable counts successes in a fixed number of independent trials with a constant success probability.
- Normal probability plot
- A normal probability plot graphs ordered data against standard normal quantiles, with a straight pattern supporting normality.
- Unbiased estimator
- An unbiased estimator is a statistic whose expected value equals the parameter it estimates.
- Confidence interval
- A confidence interval is a range of plausible values for a parameter, built as a point estimate plus or minus a margin of error.
STAT1008 FAQ
How is the final mark made up?
Five tasks contribute. An online quiz in Week 4 and an in-tutorial probability quiz in Week 5 are worth 5% each, an in-tutorial Excel quiz in Week 6 is worth 10%, a group presentation in Weeks 9 to 12 is worth 15%, and the in-person final exam in the examination period carries the remaining 65%.
What is known about the final exam format?
The course materials describe the final exam as an in-person, two-hour paper that is compulsory and covers the whole syllabus. A calculator is provided in the exam, the standard normal table is the course’s cumulative table, and the lecturer states that the paper will say when a continuity correction should be used.
How difficult is this course?
The materials point to two pressures rather than any single hard topic. Sixty-five per cent of the grade rests on one two-hour paper covering every week, and probability, distributions and inference build on each other, so a gap early on resurfaces later. Hand calculation with a calculator, not software, is what the exam tests.
How much mathematics is involved?
The algebra is introductory, but the course is quantitative throughout. Expect sums, square roots, combinations, standardising with z, reading cumulative tables and solving simple equations for an unknown mean, standard deviation or sample size. Accuracy to four decimal places and clear working matter as much as the algebra itself.
Are past exam papers included in this guide?
This guide does not reproduce past exam papers. Its practice questions are newly written and follow the question types of the tutorials, workshops and the written probability quiz, including its one-problem, five-part structure, without reproducing any of them.
How is Excel used in assessment?
Excel with the Analysis ToolPak is the course’s statistical software. The Week 6 in-tutorial quiz is a closed-book Excel data analysis task on the lab computer, and the group presentation requires an exact p-value calculated with an Excel function such as T.DIST or NORM.S.DIST.
What is a good revision plan for the final weeks?
Work chapter by chapter in course order, solving each worked example on paper before checking it in Excel. Keep a log of specific slips, rehearse the confidence-interval sentence until it is automatic, and set aside time for the later weeks on hypothesis testing and regression, since the final exam covers the whole syllabus.
Questions students ask in each STAT1008 chapter
- What is the difference between a parameter and a statistic?
- A parameter describes the whole population and is usually unknown, such as the true mean income of all adults. A statistic is calculated from the sample you collected, such as the mean income of 200 surveyed people, and serves as its estimate. Chapter 01 · Populations, Samples and Data Collection
- How do I know whether to use row or column percentages?
- Ask which variable is the condition in the question. If you want to compare groups defined by the rows, divide each cell by its row total. If the groups are the columns, use column totals. Grand-total percentages describe the joint distribution of both variables. Chapter 02 · Tables and Charts for Summarising Data
- Should I report the mean or the median?
- Look at the shape first. For roughly symmetric data the mean and standard deviation summarise well. For skewed data or data with extreme values, the median and interquartile range are better, because a single large value can pull the mean a long way. Chapter 03 · Measures of Centre, Variation and Shape
- Why do my quartiles differ from Excel’s?
- Excel’s PERCENTILE.INC and PERCENTILE.EXC use their own location formulas and interpolate between values, while the course’s hand rule averages or rounds up. On small datasets the results differ slightly. The lecture accepts either Excel function unless one is specified. Chapter 04 · Quartiles, Boxplots and Outliers
- Are mutually exclusive events independent?
- No, unless one has probability zero. If two events cannot happen together, learning that one occurred tells you the other did not, which changes its probability to zero. Independence requires the probability to stay the same. Chapter 05 · Probability Rules and Contingency Tables
- How do I know whether a question needs Bayes’ theorem?
- Look for a reversed condition. If the stem gives probabilities of evidence given each cause, and asks for the probability of a cause given the evidence, Bayes’ theorem is the tool. A probability tree makes the same calculation visible. Chapter 06 · Conditional Probability, Bayes and Counting
- Is the expected value the same as the sample mean?
- No. The expected value is computed from the probability distribution before any data are seen and is a parameter. The sample mean is computed from observed data, weights each observation equally and serves as an estimate of the expected value. Chapter 07 · Discrete Random Variables and Expected Value
- How do I show that a situation is binomial?
- Check the four properties in the context of the question: a fixed number of trials, two outcomes on each trial, the same success probability every time, and independence between trials. Name each one with the scenario’s details. Chapter 08 · The Binomial Distribution
- Why is the probability of an exact value zero for a continuous variable?
- Probability for a continuous variable is area under the density curve, and a single point has no width, so its area is zero. That is also why P(X less than a) and P(X at most a) are equal for a continuous variable. Chapter 09 · Normal and Uniform Distributions
- Does the Central Limit Theorem make the data normal?
- No. It describes the distribution of the sample mean, not of individual observations. A skewed population stays skewed, but the average of a large independent sample from it is approximately normal. Chapter 10 · Sampling Distributions and the Central Limit Theorem
- Does a 95% interval have a 95% chance of containing the mean?
- Not in the course’s interpretation. Once calculated, an interval either contains the parameter or it does not. The 95% describes the method: over many repeated samples, about 95% of intervals built this way would capture the true mean. Chapter 11 · Confidence Intervals for Means and Proportions
How to study for the exam
Revise STAT1008 as one connected chain rather than a list of topics. Begin with the language of data: population, sample, parameter, statistic, design and error, because almost every multi-part question opens with them. Next rebuild the descriptive toolkit by hand, from frequency tables and percentages to means, standard deviations, quartiles and boxplots, checking each result in Excel.
In probability, define events in letters, write the rule you are using, and give answers to four decimal places. For each distribution, practise stating the model with its parameters before calculating, and sketch the normal curve before every table look-up. In inference, decide first whether a question is about one observation or a sample mean, then build intervals with the six-line routine and the prescribed sentence.
Keep a correction log of precise slips, and in the final fortnight rehearse full mixed questions under a two-hour limit, leaving time for the later weeks of the syllabus.
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