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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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Construct complete boxplots · Check your progress
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Construct complete stem-and-leaf plots · Check your progress
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Estimate grouped means · Check your progress
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Calculate whole-data standard deviations · Check your progress
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Estimate grouped standard deviations · Check your progress
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Find combined-event probabilities · Check your progress
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Read cumulative frequency in reverse · 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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Construct complete boxplots · Check again
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Construct complete stem-and-leaf plots · Check again
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Estimate grouped means · Check again
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Calculate whole-data standard deviations · Check again
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Estimate grouped standard deviations · Check again
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Find combined-event probabilities · Check again
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Read cumulative frequency in reverse · 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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Construct complete boxplots · Retention check
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Construct complete stem-and-leaf plots · Retention check
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Estimate grouped means · Retention check
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Calculate whole-data standard deviations · Retention check
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Estimate grouped standard deviations · Retention check
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Find combined-event probabilities · Retention check
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Read cumulative frequency in reverse · 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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Practise: Construct complete boxplots
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Practise: Construct complete stem-and-leaf plots
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Practise: Estimate grouped means
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Practise: Calculate whole-data standard deviations
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Practise: Estimate grouped standard deviations
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Practise: Find combined-event probabilities
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Practise: Read cumulative frequency in reverse
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Next step
Revision notes
Read and compare statistical displays and spread in G3 Mathematics, distinguishing estimates, independent events and conditional probabilities.
Key ideas
- Collect data and make a table
Organise observations into a frequency table, choose a suitable display and check what the data can support.
- Histograms and dot diagrams
Use numerical intervals for a histogram and one mark per observation for a dot diagram.
- Mean, median and mode
Choose a measure for the question and sort the values before finding positional summaries.
- 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.
- Stem-and-leaf plots and grouped means
Preserve exact values where possible and label estimates that use class midpoints.
- Quartiles, percentiles and cumulative frequency
Read cumulative counts at class boundaries and treat grouped-data interpolation as an estimate.
- Boxplots and spread comparisons
Construct the five-number summary on one scale and state what it cannot recover.
- Standard deviation and data comparison
Measure spread around the mean and distinguish an exact data calculation from a grouped-data estimate.
- Single-event probability
List the sample space and justify equal likelihood before counting favourable outcomes.
- Combined events and conditional branches
Distinguish mutually exclusive events from independent events and multiply probabilities along a stated branch.
Common mistakes
Mistake Independent events cannot happen together.
Correct idea Mutually exclusive events cannot happen together, so P(A and B) = 0. Independent events can happen together: one happening does not change the probability of the other, so P(A and B) = P(A) × P(B). For example, getting a head when tossing a coin and a 6 when rolling a die are independent and can happen together.
From the G3 Mathematics 2027 syllabus
Show all 16 syllabus statements
- 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)