Statistics and probability
Build and connect the representations and methods in statistics and probability.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
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
- 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)
- 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 use 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
Work through them in order.
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 tableG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020 · Express Secondary 3–4 Mathematics 2022Organise observations into a frequency table, choose a suitable display and check what the data can support.
- Histograms and dot diagramsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Use numerical intervals for a histogram and one mark per observation for a dot diagram.
- Mean, median and modeG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Choose a measure for the question and sort the values before finding positional summaries.
- Stem-and-leaf plots and grouped meansG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Preserve exact values where possible and label estimates that use class midpoints.
- Quartiles, percentiles and cumulative frequencyG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Read cumulative counts at class boundaries and treat grouped-data interpolation as an estimate.
- Boxplots and spread comparisonsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Construct the five-number summary on one scale and state what it cannot recover.
- Standard deviation and data comparisonG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Measure spread around the mean and distinguish an exact data calculation from a grouped-data estimate.
- Single-event probabilityG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021List the sample space and justify equal likelihood before counting favourable outcomes.
- Combined events and conditional branchesG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Distinguish mutually exclusive events from independent events and multiply probabilities along a stated branch.
No lessons match your search. Try a shorter phrase, or show all lessons.