GEA1000 Quantitative Reasoning with Data
The Complete Exam Bible · Sem 1 AY26/27GEA1000 Overview
- National University of Singapore
- Semester 1 AY2026/27
- Level 1
- 4 units
- In-person blended teaching
What this course trains
GEA1000 treats quantitative reasoning as a complete path from question to conclusion. The course asks who a claim is about, how the data were obtained, what kind of variable was measured, which comparison answers the question, and how uncertainty changes the final sentence.
- Final examination The final examination carries 45% and the revised circular specifies twelve questions worth twenty marks in ninety minutes.
- Coursework route Participation, a group data project and six repeated-attempt quizzes together carry 55% of the grade.
- Hardest decision Most errors begin before calculation, when a denominator, sampling frame or comparison direction is selected.
- Exam preparation Build the permitted double-sided A4 helpsheet from mistakes, with interpretation wording beside every formula.
How GEA1000 is assessed
| Component | Weight | Format |
|---|---|---|
| Tutorial participation | 15% | Attendance and active participation in classes. |
| Group project | 30% | Evaluate a quantitative study, analyse a supplied data set using software and answer research questions. |
| Online quizzes | 10% | Six quizzes across the semester, with repeated attempts and the best score retained for each quiz. |
| Final Examination | 45% | In-person secure digital exam on 21 November 2026 at 1pm; ninety minutes, twelve questions and twenty marks. |
The four published weights total 100%. The revised second examination circular supersedes the earlier question count and supplies the current duration, question structure, mark total and permitted materials.
Current GEA1000 dates
| Date | Item | Control |
|---|---|---|
| 23 August 2026 | Quiz 1 due | Chapter 1 quiz due by 23:59. |
| 6 September 2026 | Quiz 2 due | Chapter 2 quiz due by 23:59. |
| 20 September 2026 | Quiz 3 due | Chapter 3 quiz due by 23:59. |
| 11 October 2026 | Quiz 4 due | Chapter 4 quiz due by 23:59. |
| 1 November 2026 | Quiz 5 due | Revision quiz due by 23:59. |
| 15 November 2026 | Quiz 6 due | Revision quiz due by 23:59. |
| 21 November 2026 | Final examination | The revised circular states a 1pm start and ninety-minute duration. |
Dates are as published in the Canvas syllabus and revised final examination circular for this offering. Confirm exact deadlines and submission settings in the live LMS.
What GEA1000 covers
Five chapters follow the course from getting data through categorical and numerical reasoning to probability, sampling distributions and statistical inference.
Getting Data: Questions, Samples and Studies
Connect the PPDAC question to a sampling frame, study design and defensible claimThe claim begins in the plan
The PPDAC cycle links a quantitative question to a target population, sampling frame, observed sample, analysis and conclusion.
- PPDAC as a question-to-conclusion cycle
- Target population and unit of observation
- Sampling frames and coverage
- Probability sampling and nonresponse
- Experiments and observational studies
- Random assignment and blinding
Categorical Data: Proportions and Confounding
Choose the denominator, compare risk and odds, then slice an aggregate associationDenominators carry the question
Marginal and joint proportions use the whole table, while conditional proportions use a restricted row or column. Risk divides outcomes by everyone in a group; odds divide outcomes by non-outcomes in that group.
- Marginal, joint and conditional proportions
- Two-way table denominators
- Risk and risk ratios
- Odds and odds ratios
- Simpson's paradox
- Confounding and stratified comparisons
Numerical Data: Summaries and Relationships
Read centre and spread with the distribution, then audit correlation and regressionSummaries keep the distribution attached
The mean and standard deviation describe centre and spread around the mean, while the median and interquartile range are more resistant to skew and extreme observations.
- Mean and median
- Variance and standard deviation
- Quartiles and interquartile range
- Histograms and boxplots
- Scatterplots and correlation
- Linear regression and aggregation
Probability and Sampling Distributions
Restrict the sample space correctly and connect repeated samples to standard errorConditions redefine the sample space
Conditional probability restricts attention to cases satisfying the known condition.
- Events and sample spaces
- Conditional probability
- Mutually exclusive events
- Independent events
- Sampling distributions
- Standard error and the Central Limit Theorem
Statistical Inference: Intervals and Tests
Build confidence intervals and finish hypothesis tests with scoped population conclusionsIntervals show precision around an estimate
A confidence interval combines a sample estimate with a margin based on standard error.
- Point estimates and standard errors
- Confidence interval construction
- Repeated-sampling interpretation
- Null and alternative hypotheses
- P-values and significance levels
- Population conclusions and practical importance
Computation matters, but a correct number attached to the wrong population or denominator remains a wrong answer.
How the syllabus is organised
The PPDAC cycle provides the frame: Problem, Plan, Data, Analysis and Conclusion. The first chapter covers data collection, sampling, variable types, experiments and observational studies.
Categorical analysis follows through tables, proportions, risk, odds, confounding and Simpson's paradox. Numerical analysis brings in centre, spread, plots, correlation and regression.
The final block moves from probability and conditional reasoning to sampling distributions, confidence intervals and hypothesis tests.
What the assessment rewards
Coursework carries just over half the grade through tutorial participation, a group project and six online quizzes. The project joins critique of a quantitative study with software analysis of a supplied data set.
The quizzes are repeatable and retain the best attempt, so they are useful for diagnosing the exact concept that failed before the final examination.
The final examination
The revised circular gives a ninety-minute secure digital examination with twelve questions worth twenty marks.
Ten one-mark questions resemble Canvas quiz formats, while two longer questions carry five marks each and may include Excel or open-ended tutorial-style work. The examination is closed book, with one double-sided A4 helpsheet and permitted calculators.
How to revise efficiently
Start each problem by naming the population, variable type and comparison.
Write the conditioning phrase before a proportion, inspect distribution shape before choosing a summary, and state hypotheses before looking at the sample direction. After calculation, return to the design and write the narrowest conclusion supported by it. That routine works across all five chapters and protects both short and long responses.
Worked example · free
Choosing the denominator before calculating
- 2Compute the exposed and unexposed risks using row totals.
- 2Divide in the stated order and interpret the outcome and groups.
Key terms
- Target Population
- The full group named in the research question and intended conclusion.
- Sampling Frame
- The operational list or mechanism through which members of the target population can be selected.
- Random Assignment
- A chance mechanism that allocates experimental units to conditions to create comparable groups.
- Conditional Proportion
- A share calculated inside a restricted row or column specified by the conditioning phrase.
- Risk Ratio
- The risk in one group divided by the risk in a comparison group.
- Odds Ratio
- The odds of an outcome in one group divided by the odds in another group.
- Confounder
- A variable related to both exposure and outcome that can supply an alternative explanation for an association.
- Standard Deviation
- A measure of the spread of numerical observations around their mean.
- Correlation Coefficient
- A unit-free measure of the direction and strength of a linear relationship.
- Conditional Probability
- The probability of an event after the sample space is restricted by a known condition.
- Standard Error
- The standard deviation of a statistic across repeated random samples of the same size.
- Confidence Interval
- A range produced by a repeated-sampling procedure to estimate an unknown population parameter.
- P-Value
- The probability under the null hypothesis of the observed statistic or one more extreme in the alternative direction.
GEA1000 FAQ
How is the course assessed?
Tutorial participation carries 15%, the group project 30%, six online quizzes 10% and the final examination 45%. The published weights sum to 100%. The project combines critique of a quantitative study with software analysis of a supplied data set and answers to research questions.
What is the final examination format?
The revised circular states ninety minutes, twelve questions and twenty marks. Ten one-mark questions resemble Canvas quiz formats such as MCQ, MRQ and fill-in-the-blank. Two longer questions carry five marks each and may include Excel tasks or open-ended reasoning seen in tutorials.
What can be taken into the final examination?
The examination is closed book, but one A4-sized helpsheet may be used on both sides and may be typed or handwritten. Calculators are permitted subject to restrictions on symbolic manipulation, communication and verbal-information storage. Rough paper is supplied at the venue.
Why does study design come before calculation?
The design determines who the result represents and which verbs the conclusion may use. Random selection addresses generalisation from a frame, while random assignment supports causal comparison inside an experiment. A sophisticated calculation cannot widen a narrow frame or convert an observational association into an experimental effect.
How should risk and odds be kept separate?
Risk divides outcomes by everyone in the group. Odds divide outcomes by non-outcomes in that group. A risk ratio compares two risks and an odds ratio compares two odds. Write both component fractions before dividing, then interpret the outcome and comparison order explicitly.
What is the safest wording for a confidence interval?
State that you are confident the named population parameter lies between the endpoints, using the confidence level and the population represented by the design. Avoid saying that a fixed parameter has that probability of lying in this realised interval; the confidence rate belongs to the repeated procedure.
What does a large p-value mean?
It means the sample does not provide sufficient evidence to reject the null hypothesis at the chosen significance level. It does not prove the null is true, show two groups are identical or establish practical irrelevance. Report the estimate or interval alongside the decision when available.
Are past examination papers included in the source folder?
The available course folder includes chapter solutions, tutorial solutions and quiz instructions, but not a file presented as a past examination paper. The revised circular says a practice paper would be supplied later. This guide therefore uses original questions modelled only on the published question formats.
Questions students ask in each GEA1000 chapter
- Why can a large sample still be misleading?
- Sample size controls chance-to-chance variability after the frame and selection process are settled. A very large sample drawn from a narrow frame can estimate that narrow group precisely while remaining systematically different from the population named in the question. Chapter 01 · Getting Data: Questions, Samples and Studies
- How is the correct denominator selected?
- Write the conditioning phrase before calculating. Out of everyone signals the grand total; among the exposed signals the exposed row; among cases signals the outcome column. The same cell can produce different proportions because the conditioned totals differ. Chapter 02 · Categorical Data: Proportions and Confounding
- When should median and interquartile range be preferred?
- They are often more informative when a distribution is strongly skewed or contains influential extremes, because they resist movement from a few unusual values. Mean and standard deviation remain useful when the inferential target or distributional shape calls for them. Chapter 03 · Numerical Data: Summaries and Relationships
- Why are reversed conditional probabilities different?
- They share the intersection in the numerator but condition on different groups. Disease given positive uses all positive results as its denominator, while positive given disease uses everyone with disease. A probability tree or count table keeps both restricted totals visible. Chapter 04 · Probability and Sampling Distributions
- What does 95% confidence mean?
- It describes the interval-producing method: across repeated random samples, about 95% of intervals constructed in the same way contain the fixed population parameter. It does not mean that 95% of individual observations lie inside one confidence interval for a mean. Chapter 05 · Statistical Inference: Intervals and Tests
How to study for the exam
Build revision around decisions rather than chapters alone. First, practise naming the population, sampling frame, variable type and study design before touching a calculator. Next, create a denominator drill in which the same cell is used for a joint proportion, a row-conditional proportion and a column-conditional proportion.
For numerical data, pair every summary with a sketch of the distribution and explain why mean with standard deviation or median with interquartile range is more informative. For probability, translate rates into counts and draw the branches. For inference, write hypotheses and the population conclusion before checking the software syntax.
Use the six repeatable quizzes as diagnostics: record the concept behind every missed item and add only that concept, formula or wording warning to the permitted helpsheet. Finish with mixed practice under time, protecting enough time for the two longer questions because together they carry half of the final examination marks.
After each long response, audit the final sentence for population, direction, uncertainty and causal scope.
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