Statistics and probability
Build and connect the representations and methods in statistics and probability.
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Before you begin
Build and connect the representations and methods in statistics and probability.
Learning goals
- Organise data and construct a suitable display
- Read and interpret data displays
- Evaluate the purposes and limitations of data displays
- Calculate and interpret the arithmetic mean
- Find and interpret the mode and median
- Estimate the mean from grouped data
- Compare variability using appropriate measures
- Calculate measures of spread
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
Syllabus statements covered
- simple concepts in collecting, classifying and tabulating data • analysis and interpretation of: ∗ tables ∗ bar graphs ∗ pictograms ∗ line graphs ∗ pie charts ∗ dot diagrams ∗ histograms with equal class intervals ∗ stem-and-leaf diagrams ∗ cumulative frequency diagrams ∗ box-and-whisker plots • purposes and uses, advantages and disadvantages of the different forms of statistical representations • drawing simple inference from statistical diagrams • explaining why a given statistical diagram leads to misinterpretation of data • mean, mode and median as measures of central tendency for a set of data • purposes and use of mean, mode and median • calculation of the mean for grouped data • quartiles and percentiles • range, interquartile range and standard deviation as measures of spread for a set of data • calculation of the standard deviation for a set of data (grouped and ungrouped) • using the mean and standard deviation to compare two sets of data Cumulative frequency diagrams, box-and-whisker plots, quartiles/percentiles, spread (range, interquartile range and standard deviation), calculating standard deviation and comparing data by mean/standard deviation are tested only in Paper 2 Section B.
- probability as a measure of chance • probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability) • probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate) • addition and multiplication of probabilities (mutually exclusive events and independent events) Combined events and addition/multiplication of probabilities are tested only in Paper 2 Section B.
- simple concepts in collecting, classifying and tabulating data
- analysis and interpretation of: • tables • bar graphs • pictograms • line graphs • pie charts
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- explaining why a given statistical diagram leads to misinterpretation of data
- analysis and interpretation of: • dot diagrams • histograms • stem-and-leaf diagrams
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- explaining why a given statistical diagram leads to misinterpretation of data
- mean, mode and median as measures of central tendency for a set of data
- purposes and uses of mean, mode and median
- calculation of the mean for grouped data
- probability as a measure of chance
- probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
- quartiles and percentiles
- range, interquartile range and standard deviation as measures of spread for a set of data
- analysis and interpretation of: • cumulative frequency diagrams • box-and-whisker plots
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- calculation of the standard deviation for a set of data (grouped and ungrouped)
- using the mean and standard deviation to compare two sets of data
- probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)
- addition and multiplication of probabilities (mutually exclusive events and independent events)
Lessons
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About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Collect data and make a tableG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 3–4 Mathematics 2022Organise observations into a frequency table, choose a suitable display and check what the data can support.
- Histograms and dot diagramsG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Use numerical intervals for a histogram and one mark per observation for a dot diagram.
- Mean, median and modeG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Choose a measure for the question and sort the values before finding positional summaries.
- Stem-and-leaf plots and grouped meansG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Preserve exact values where possible and label estimates that use class midpoints.
- Quartiles, percentiles and cumulative frequencyG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Read cumulative counts at class boundaries and treat grouped-data interpolation as an estimate.
- Boxplots and spread comparisonsG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Construct the five-number summary on one scale and state what it cannot recover.
- Standard deviation and data comparisonG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Measure spread around the mean and distinguish an exact data calculation from a grouped-data estimate.
- Single-event probabilityG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021List the sample space and justify equal likelihood before counting favourable outcomes.
- Combined events and conditional branchesG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Distinguish mutually exclusive events from independent events and multiply probabilities along a stated branch.
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