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• VCMMG169

  Compare the areas of regular and irregular shapes by informal means

  Elaborations

  • comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares

  VCMMG169 | Mathematics | Level 4 | Measurement and Geometry | Shape

• VCMSP271

  Describe and interpret data displays using median, mean and range

  Elaborations

  • using mean and median to compare data sets and explaining how outliers may affect the comparison
  • locating mean, median and range on graphs and connecting them to real life

  VCMSP271 | Mathematics | Level 7 | Statistics and Probability | Data representation and interpretation

• VCMSP299

  Explore the variation of means and proportions of random samples drawn from the same population

  Elaborations

  • using sample properties to predict characteristics of the population

  VCMSP299 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMSP300

  Investigate the effect of individual data values including outliers, on the range, mean and median

  Elaborations

  • using displays of data to explore and investigate effects
  • exploring the effect of outliers on the range for different sets of data by comparing its value with and without outliers included

  VCMSP300 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMSP270

  Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data

  Elaborations

  • understanding that summarising data by calculating measures of centre and spread can help make sense of the data

  VCMSP270 | Mathematics | Level 7 | Statistics and Probability | Data representation and interpretation

• VCMSP323

  Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians

  Elaborations

  • investigating a range of data and its sources. For example, the age of residents in Australia, Cambodia and Tonga, or the number of subjects studied at school by 14-year-old students in Australia, Japan and Timor-Leste

  VCMSP323 | Mathematics | Level 9 | Statistics and Probability | Chance

• VCMSP326

  Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread

  Elaborations

  • comparing means, medians and ranges of two sets of numerical data which have been displayed using histograms, dot plots, or stem and leaf plots

  VCMSP326 | Mathematics | Level 9 | Statistics and Probability | Data representation and interpretation

• VC2M10AST01

  calculate and interpret the mean and standard deviation of data and use these to compare data sets; investigate the effect of individual data values, including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VC2M10AST01 | Mathematics | Mathematics Version 2.0 | Level 10A | Statistics

• VCMSP372

  Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VCMSP372 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• VC2M7ST01

  acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data

  Elaborations

  • understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures
  • comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics
  • recognising how different data sets can have the same measures of central tendency and experimenting with how varying data affects these measures
  • acquiring continuous numerical data by taking measurement samples during a science experiment, observation or field study, comparing measures of central tendency and identifying any anomalies in the distribution of data

  VC2M7ST01 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M9ST01

  analyse reports of surveys in digital media and elsewhere for information on how data was obtained around everyday questions and issues involving at least one numerical and at least one categorical variable, to estimate population means and medians

  Elaborations

  • investigating and evaluating statistical reports in the media and other places by linking claims to displays, statistics and representative data
  • investigating the use of statistics in reports regarding the growth of Australia’s trade with other countries of the Asia region
  • investigating a range of data and its sources, for example, the age of residents in Australia, Cambodia and Tonga, or the number of subjects studied at school in a year by 14-year-old students in Australia, Singapore, Japan, South Korea and Timor-Leste
  • analysing reports of public opinion surveys on environmental issues, such as land clearing, wind farms or single-use plastics, discussing methods of data collection and the reasonableness of any inferences made
  • comparing the annual rainfall in various parts of Australia, Pakistan, New Guinea and Malaysia

  VC2M9ST01 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M7ST02

  create different types of displays of numerical data, including dot plots and stem-and-leaf plots, using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

  Elaborations

  • using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
  • comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe ‘symmetry’, ‘skewness’ and ‘average’ in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
  • connecting features of the data display (for example, highest frequency, clusters, gaps, symmetry or skewness) to the mode, range and median, and the question in context; describing the shape of distributions using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’ and discussing the location of the median and mean on these distributions
  • using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
  • comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value

  VC2M7ST02 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M9ST03

  represent the distribution of multiple data sets for numerical variables using comparative representations such as back-to-back stem-and-leaf plots and histograms; describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’; compare data distributions using mean, median and range...

  Elaborations

  • describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’
  • using stem-and-leaf plots to compare 2 like sets of data such as the heights of girls and the heights of boys in a class
  • constructing grouped histograms that show trends in health issues such as lung cancer, leukaemia, stroke and diabetes, and using the graph to justify, verify or invalidate claims
  • exploring comparative data presented in reports by the National Indigenous Australians Agency in regard to ‘Closing the Gap’, discussing the comparative distributions within the context of the data, for example, comparative data presented in the ‘Closing the Gap – Prime Minister’s Report’ 
  • comparing means, medians and ranges of 2 sets of numerical data that have been displayed using histograms, dot plots or stem-and-leaf plots

  VC2M9ST03 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• Mathematics: Level 7 achievement standards

  Number and Algebra

  Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions...

  Level description | Mathematics | Level 7

• VCMNA307

  Apply set structures to solve real-world problems

  Elaborations

  • using a sort algorithm to determine the median of a set of numbers
  • exploring variation in proportion and means of random samples, drawn from a population

  VCMNA307 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• Mathematics | Mathematics Version 2.0: Structure

  Mathematics is presented in 11 levels, from Foundation to Level 10.

  Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

  Strands

  The curriculum is organised into 6 interrelated...

  Overview material | Mathematics Version 2.0

• VC2M10AST02

  identify measures of spread, and understand their interpretation and usefulness with respect to different data distributions

  Elaborations

  • comparing the use of quantiles, percentiles, and cumulative frequency to analyse the distribution of data
  • comparing measures of spread for different data distributions, such as mean or median absolute deviations with standard deviations, and exploring the effect of outliers

  VC2M10AST02 | Mathematics | Mathematics Version 2.0 | Level 10A | Statistics

• VCMSP266

  Construct sample spaces for single-step experiments with equally likely outcomes

  Elaborations

  • discussing the meaning of probability terminology. For example, probability, sample space, favourable outcomes, trial, events and experiments
  • distinguishing between equally likely outcomes and outcomes that are not equally likely

  VCMSP266 | Mathematics | Level 7 | Statistics and Probability | Chance

• Mathematics: Level 8 achievement standards

  Number and Algebra

  Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday...

  Level description | Mathematics | Level 8

• Mathematics: Level 9 achievement standards

  Number and Algebra

  Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students...

  Level description | Mathematics | Level 9