Back to Statistics and probability

Data displays, summaries, quantiles and single-event probability topic check

Practise data displays, summaries, quantiles and single-event probability in G1 Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals
  • Read and interpret quantities in a bar graph
  • Read observations and changes on a line graph
  • Interpret sector shares relative to a pie chart's whole
  • Find quartiles and interquartile range under a stated finite-data convention
  • Estimate quartiles, a percentile and interquartile range by linear interpolation
  • Read and interpret data displays
  • Organise data and construct a suitable display
  • Evaluate the purposes and limitations of data displays
  • Calculate and interpret the arithmetic mean
  • Find and interpret the mode and median
  • Find the median of ungrouped observations
  • Find every mode of ungrouped observations
  • Calculate the range of ungrouped observations
  • Compare variability using appropriate measures
  • Count all and qualifying uniform outcomes and calculate the event probability
  • G1 Mathematics 2027
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Check your progress

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Calculate arithmetic means · Check your progress

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Find medians · Check your progress

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Find every mode · Check your progress

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Calculate ranges · Check your progress

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Count single-event probabilities · Check your progress

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Find quartiles and interquartile range · Check your progress

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Estimate grouped percentiles · Check your progress

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Read bar charts · Check your progress

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Read line graphs · Check your progress

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Read pie charts · Check your progress

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Read dot diagrams, histograms and pictograms · Check your progress

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Check again

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Calculate arithmetic means · Check again

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Find medians · Check again

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Find every mode · Check again

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Calculate ranges · Check again

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Count single-event probabilities · Check again

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Find quartiles and interquartile range · Check again

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Estimate grouped percentiles · Check again

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Read bar charts · Check again

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Read line graphs · Check again

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Read pie charts · Check again

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Read dot diagrams, histograms and pictograms · Check again

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Retention check

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Calculate arithmetic means · Retention check

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Find medians · Retention check

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Find every mode · Retention check

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Calculate ranges · Retention check

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Count single-event probabilities · Retention check

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Find quartiles and interquartile range · Retention check

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Estimate grouped percentiles · Retention check

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Read bar charts · Retention check

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Read line graphs · Retention check

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Read pie charts · Retention check

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Read dot diagrams, histograms and pictograms · Retention check

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Practise: Calculate arithmetic means

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Practise: Find medians

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Practise: Find every mode

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Practise: Calculate ranges

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Practise: Count single-event probabilities

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Practise: Find quartiles and interquartile range

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Practise: Estimate grouped percentiles

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Practise: Read bar charts

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Practise: Read line graphs

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Practise: Read pie charts

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Practise: Read dot diagrams, histograms and pictograms

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Revision notes

Revise statistics and probability

Organise data in tables, histograms and dot diagrams, interpret averages and cumulative frequency, and calculate single-event probabilities.

Key ideas

  1. Collect data and make a table

    Organise observations into a frequency table, choose a suitable display and check what the data can support.

  2. Histograms and dot diagrams

    Use numerical intervals for a histogram and one mark per observation for a dot diagram.

  3. Mean, median and mode

    Choose a measure for the question and sort the values before finding positional summaries.

  4. Recover the data before finding a summary

    Recover individual frequencies from running totals or a removed group, then find a mean, median, mode or range.

  5. Quartiles, percentiles and cumulative frequency

    Read cumulative counts at class boundaries and treat grouped-data interpolation as an estimate.

  6. Single-event probability

    List the sample space and justify equal likelihood before counting favourable outcomes.

What the syllabus asks

From the G1 Mathematics 2027 syllabus

  • 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 ∗ cumulative frequency diagrams
  • Purposes and use, advantages and disadvantages of the different forms of statistical representations
  • Purposes and use of mean, mode and median
  • Calculation of the mean, mode and median for a set of ungrouped data
  • Percentiles, quartiles, range and interquartile range
  • 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)