About this topic
Before you begin
Read and compare statistical displays and spread in G3 Mathematics, distinguishing estimates, independent events and conditional probabilities.
Learning goals
- Organise data and construct a suitable display
- Read and interpret data displays
- Evaluate the purposes and limitations of data displays
- 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
- Calculate and interpret the arithmetic mean
- Find the median of ungrouped observations
- Find every mode of ungrouped observations
- Find and interpret the mode and median
- Calculate the range of ungrouped observations
- Construct a complete ordered single-sided stem-and-leaf plot with a key
- Estimate the mean from grouped data
- Find quartiles and interquartile range under a stated finite-data convention
- Estimate quartiles, a percentile and interquartile range by linear interpolation
- Estimate how many and what percentage of grouped observations lie below or above a value
- Compare variability using appropriate measures
- Construct a complete minimum-to-maximum boxplot on an exact rational scale
- Calculate whole-data standard deviation from values and frequencies
- Estimate standard deviation from grouped data
- Calculate measures of spread
- Count all and qualifying uniform outcomes and calculate the event probability
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
- Calculate two-stage event probabilities from possibility tables or tree routes
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)
Choose a lesson
Work through them in order.
- Not startedCollect data and make a tableNextOrganise observations into a frequency table, choose a suitable display and check what the data can support.
- Not startedHistograms and dot diagramsNextUse numerical intervals for a histogram and one mark per observation for a dot diagram.
- Not startedMean, median and modeNextChoose a measure for the question and sort the values before finding positional summaries.
- Not startedRecover the data before finding a summaryNextRecover individual frequencies from running totals or a removed group, then find a mean, median, mode or range.
- Not startedStem-and-leaf plots and grouped meansNextPreserve exact values where possible and label estimates that use class midpoints.
- Not startedQuartiles, percentiles and cumulative frequencyNextRead cumulative counts at class boundaries and treat grouped-data interpolation as an estimate.
- Not startedBoxplots and spread comparisonsNextConstruct the five-number summary on one scale and state what it cannot recover.
- Not startedStandard deviation and data comparisonNextMeasure spread around the mean and distinguish an exact data calculation from a grouped-data estimate.
- Not startedSingle-event probabilityNextList the sample space and justify equal likelihood before counting favourable outcomes.
- Not startedCombined events and conditional branchesNextDistinguish mutually exclusive events from independent events and multiply probabilities along a stated branch.
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