MGU · MG1DSCSTA100 · Companion resource

Fundamentals of Statistics and Data Visualisation

Revision and exam practice

Use these checklists to find gaps, then return to the worked explanations in the main study guide. Every suggested question is syllabus-based practice, not a claim about an actual or guaranteed MGU question.

4 MODULES · THEORY + PRACTICAL · SELF-CHECK

How the priorities were chosen

The syllabus gives 15 hours each to Modules 1, 2 and 3, and 30 hours to spreadsheet work in Module 4. Its outcomes explicitly require summarising data, analysing relationships, applying regression and Bayes’ theorem, and using spreadsheets. The ESE format specifies 2-, 6- and 12-mark responses. The priority labels below reflect those syllabus facts; they do not assign guessed marks to individual topics.

MUST MASTER

Raw-data summaries, correlation/regression interpretation, probability applications, and spreadsheet problem solving. These directly support stated outcomes and numerical/application work.

IMPORTANT

Data collection, scales, sampling, distribution shape, probability definitions and graph selection. They build the concepts used in the core applications.

QUICK-SCORE

Definitions, distinctions, stated properties, formula symbols and interpretation vocabulary. Prepare concise and accurate explanations.

SCOPE CHECK

Sampling derivations are not required; correlation properties and concepts are required without proof; Bayes’ theorem is included without proof. Module 5 lists teacher-specific content but gives no topics in the supplied syllabus.

MODULE 1 · 15 HOURS

Data and descriptive statistics

Priority path: first classify data and sampling; next practise centres and spread; then explain graphs, box plots and shape.

10 core concepts

  1. Primary vs secondary data
  2. Univariate vs bivariate observations
  3. Bar, pie and frequency displays
  4. Nominal scale
  5. Ordinal scale
  6. Interval scale
  7. Ratio scale
  8. Population, sample and sampling
  9. Centre and dispersion
  10. Moments, skewness and kurtosis

10 key terms

Variable · observation · frequency · nominal · ordinal · interval · ratio · population · sample · quartile

Also define: deviation, moment, skewness, kurtosis, box plot and coefficient of variation when a question requires them.

Formula and method checklist

Be able to state and use AM, GM, HM, median, mode, range, QD, MD, SD, CV and pie-sector angle formulas. Know the symbols, restrictions (e.g. positive values for the ordinary GM), and the data-ordering steps for median and quartiles. State the quartile and SD convention used when relevant.

Common traps: calculate median/quartiles from ordered values; use absolute deviations for MD; square deviations before summing for SD; distinguish ratio from interval zero; stratified sampling selects from every stratum while cluster sampling selects clusters.

Expected / Exam-Focused Questions based on the syllabus

  • 2 marks: Define bivariate data; distinguish interval and ratio scales; define QD or CV.
  • 6 marks: Explain the four scales; compare sampling methods; calculate and interpret central tendency or dispersion for raw data.
  • 12 marks: Summarise a supplied raw data set with suitable measures and interpret; explain sampling and data displays with examples.
  • Numerical: calculate AM/GM/HM/median/mode; range/QD/MD/SD/CV; pie-sector angles; read a box plot.
  • Conceptual: why can mean and median differ? Which scale permits meaningful ratios? Why can SD and CV tell different comparison stories?

Module self-check

MODULE 2 · 15 HOURS

Correlation and regression

Priority path: read the scatter first; calculate and interpret a coefficient; choose the regression line that matches the requested prediction.

10 core concepts

  1. Paired observations
  2. Scatter diagram
  3. Positive association
  4. Negative association
  5. Strength of linear association
  6. Karl Pearson’s r
  7. Spearman’s rank coefficient
  8. Regression of y on x
  9. Regression of x on y
  10. Prediction and its limits

10 key terms

Pair · scatter · association · linear · coefficient · rank · tied rank · regression · slope · prediction

Remember: correlation describes association; regression fits a line for estimating one variable from another.

Formula and method checklist

Know the Pearson product-moment formula and the range −1 to +1. Know the Spearman formula for untied ranks, how to rank each variable, and how to calculate d and d². For regression, know both line forms and slopes; centre the data using x̄ and ȳ. The syllabus requires concepts, problems and properties without proof.

Common traps: correlation does not prove cause; r near zero rules out neither a curved nor another kind of association; select y on x to estimate y from known x; do not extrapolate without caution; ties require appropriate handling.

Expected / Exam-Focused Questions based on the syllabus

  • 2 marks: State the range of r; define regression; what does a negative correlation indicate?
  • 6 marks: Explain Pearson’s or Spearman’s coefficient and interpret it; describe the two regression lines.
  • 12 marks: Analyse paired data using a scatter diagram, a correlation measure and an appropriate regression line; interpret the estimate and limitations.
  • Numerical: calculate Pearson r; rank pairs and calculate Spearman rₛ; find a regression line and estimate within the observed range.
  • Commonly confused: association vs causation; Pearson vs Spearman; y-on-x vs x-on-y; correlation coefficient vs regression slope.

Module self-check

MODULE 3 · 15 HOURS

Elementary probability theory

Priority path: define outcomes/events; practise basic probability; then work on conditional probability, independence, total probability and Bayes in that order.

10 core concepts

  1. Random experiment
  2. Outcome
  3. Sample space
  4. Event
  5. Frequency definition
  6. Classical definition
  7. Axiomatic definition
  8. Conditional probability
  9. Independence
  10. Total probability and Bayes update

10 key terms

Experiment · outcome · sample space · event · complement · equally likely · conditional · independent · partition · posterior

“Posterior” means an updated probability after evidence; it is a plain-language aid to understanding Bayes’ theorem.

Formula and method checklist

Know P(A)=favourable/total for equally likely outcomes; complement; conditional probability; the independence product rule; total probability for a partition; and Bayes’ theorem. Always check that the conditioning event has non-zero probability and that the cases form a complete, non-overlapping partition.

Common traps: P(A|B) is not P(B|A); count only outcomes consistent with the condition; different events are not automatically independent; calculate total evidence probability before applying Bayes.

Expected / Exam-Focused Questions based on the syllabus

  • 2 marks: Define a sample space; state conditional probability; define independent events.
  • 6 marks: Explain the three probability definitions; distinguish conditional probability and independence with an example.
  • 12 marks: Explain and apply conditional probability, total probability and Bayes’ theorem to a contextual example; proofs are not required by the syllabus.
  • Numerical: list outcomes, compute event probabilities, test independence, solve a partition/tree and update using Bayes.
  • Commonly confused: outcome vs event; mutually exclusive vs independent; P(A|B) vs P(B|A); prior vs updated probability.

Module self-check

MODULE 4 · 30 HOURS

Spreadsheet problem solving

Priority path: practise the spreadsheet operations alongside the relevant theory. The syllabus allocates 30 hours to this module and requires a practical record with at least five problems.

10 core skills

  1. Recognise rows, columns and cells
  2. Enter observations consistently
  3. Label variables and units
  4. Select a cell range
  5. Use arithmetic formulas
  6. Use descriptive-statistic functions
  7. Make a frequency table
  8. Create a suitable chart
  9. Analyse paired data
  10. Record and interpret output

10 key terms

Workbook · worksheet · cell · cell reference · range · formula · function · chart · output · interpretation

Function names can vary across spreadsheet programs and versions. Use the functions available in your lab software.

Practical record checklist

Include at least five syllabus-related problems. For each, record the problem, input data, formula/function or steps, output, interpretation and a check. Keep the original observations separate from calculated results. Use graphs with titles, labelled axes and units.

Common traps: selecting an incomplete cell range; sorting one column without its paired values; mixing text with numeric cells; using population SD when the requested convention is sample SD (or vice versa); pasting a result without explaining it.

Expected / Exam-Focused and viva questions

  • 2 marks: Define a cell range; what is a spreadsheet function?
  • 6 marks: Describe how to calculate and check a descriptive measure or create a graph using a spreadsheet.
  • 12 marks / practical: analyse supplied data with appropriate spreadsheet calculations and display, then interpret the output.
  • Viva: What is a cell reference? How do you verify a function range? Why preserve the raw data? Which chart suits categories? What does the chart tell you?

Module self-check

REVISION SYSTEM

7-day and 14-day study plans

Use active recall: close your notes, explain an idea, solve a problem, then check. Adjust study hours to your schedule; each day has a concrete outcome rather than an assumed number of hours.

7-day focused revision

DayFocusFinish with
1Data types, graphs, scales, population and samplingOne-page comparison table; self-test definitions
2Central tendencyRaw-data examples for AM, GM, HM, median and mode
3Dispersion, box plots, moments and shapeOne complete dispersion problem and interpretation
4Correlation and ranksOne Pearson and one untied Spearman problem
5RegressionBoth line forms, prediction and limitation explanation
6ProbabilityBasic, conditional, independence, total probability and Bayes practice
7Spreadsheets and mixed exam practiceCheck five-record requirement; timed answers and error review

14-day steady revision

DayFocus
1Univariate/bivariate data; primary/secondary data; variable examples
2Graphs and four scales; explain examples aloud
3Population, sample and sampling comparisons
4AM, GM, HM, median and mode; easy then moderate raw data
5Range, quartiles, QD and box plots
6MD, SD, CV; interpretation and common mistakes
7Moments, skewness and kurtosis; Module 1 retrieval quiz
8Scatter diagrams and Pearson correlation
9Spearman ranks, including ranking practice; revise Module 2
10Regression lines and predictions; limitations
11Experiments, sample spaces and probability definitions
12Conditional probability and independence
13Total probability, Bayes, spreadsheet practical tasks
14Mixed timed paper-style questions, answer writing and final error review

Final 24-hour checklist

Use the final hours for recall and correcting small gaps. Avoid beginning advanced material outside the syllabus.

FINAL COURSE CHECK

If you can do these things, you are exam ready

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