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• VC2M5ST02

  interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made

  Elaborations

  • reading and interpreting different line graphs, discussing how the horizontal axis represents measures of time such as days of the week or times of the day, and the vertical axis represents numerical quantities or ordinal categorical variables such as percentages, money, measurements or ratings such as fire hazard ratings
  • interpreting real-life data represented as a line graph showing how measurements change over a period of time, and make simple inferences
  • matching unlabelled line graphs to the context they represent based on the stories of the different contexts
  • interpreting the data represented in a line graph, making inferences; for example, reading line graphs that show the varying temperatures or ultraviolet (UV) rates over a period of a day and discussing when would be the best time to hold an outdoor assembly

  VC2M5ST02 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M7ST03

  plan and conduct statistical investigations for issues involving discrete and continuous numerical data, and data collected from primary and secondary sources; analyse and interpret distributions of data and report findings in terms of shape and summary statistics

  Elaborations

  • obtaining secondary data from newspapers, the internet or the Australian Bureau of Statistics
  • investigating secondary data relating to the distribution and use of non-renewable resources around the world
  • conducting an investigation to draw conclusions about whether teenagers have faster reaction times than adults
  • conducting an investigation to support claims that a modification of a science, technology, engineering and mathematics (STEM) related design has improved performance
  • using secondary data from the Australian Reconciliation Barometer to conduct and report on statistical investigations relating to Aboriginal and Torres Strait Islander Peoples

  VC2M7ST03 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M8ST03

  compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

  Elaborations

  • comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
  • using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
  • using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
  • investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
  • investigating Aboriginal and/or Torres Strait Islander ranger groups and other groups’ use of sampling techniques to track biodiversity of species

  VC2M8ST03 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M9ST05

  plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

  Elaborations

  • planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
  • planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
  • investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
  • posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables

  VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M10ST01

  compare data distributions for continuous numerical variables using quartiles and interquartile range and appropriate data displays including boxplots, histograms and dot plots; discuss the shapes of these distributions in terms of centre, spread, shape and outliers in the context of the data

  Elaborations

  • finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the boxplot, as tools for both numerically and visually comparing the centre and spread of data sets
  • exploring the effect of varying data values, including outliers, on the interquartile range for different sets of data
  • constructing and interpreting boxplots and using them to compare data sets, understanding that boxplots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
  • comparing shapes of distributions using boxplots, histograms, cumulative frequency graphs and dot plots, discussing symmetry, skew and modality
  • using digital tools to compare boxplots and histograms as displays of the same data in the light of the statistical questions being addressed and the effectiveness of the display in helping to answer the question
  • comparing the information that can be extracted and the stories that can be told about continuous and discrete numerical data sets that have been displayed in different ways, including histograms, dot plots, boxplots and cumulative frequency graphs

  VC2M10ST01 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M2ST02

  create different graphical representations of data using software where appropriate; compare the different representations, and identify and describe common and distinctive features in response to questions

  Elaborations

  • collecting data from a limited list of choices, creating 2 different graphical representations of the data, and discussing and comparing the different representations; for example, asking the class to choose their favourite colour from a given set, then co-creating a picture graph with colours on the horizontal axis and comparing it to a column graph with colours on the horizontal axis and numbers on the vertical axis
  • creating different data displays (for example, lists, tally charts, jointly created column graphs and picture graphs) to represent a data set, describing the information that each display represents and discussing how easy or hard they are to interpret and why
  • using digital tools to create picture graphs to represent data using one-to-one correspondence, deciding on an appropriate title for the graph and considering whether the categories of data are appropriate for the context
  • comparing picture graphs with one-to-one column graphs of the same data, interpreting the data in each and saying how they are the same and how they are different; for example, collecting data on the country of birth of each student and creating different pictographs to represent classroom data
  • using dot plots, sticker charts, picture graphs, bar charts and column graphs to represent data

  VC2M2ST02 | Mathematics | Mathematics Version 2.0 | Level 2 | Statistics

• VC2M4ST02

  analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data

  Elaborations

  • suggesting questions that can be answered by a given data display and using the display to answer these questions
  • interpreting data representations in the media and other forums where symbols represent one-to-many relationships and how this can be challenging when the representations use part-whole representations
  • comparing different student-generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data

  VC2M4ST02 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• VC2M4ST03

  conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results

  Elaborations

  • creating a survey to collect class responses to a preferred movie choice, and recording data responses using spreadsheets; graphing data using a column graph or other appropriate representations; and interpreting the results of the survey and reporting findings back to the class
  • conducting a statistical investigation and acquiring data from different online sources; for example, using online query interfaces to select and retrieve data from an online database such as weather records, data frequency mapping software such as Google Trends, or the World Health Organization
  • investigating different contexts in which statistical investigations can take place and the types of questions to ask to collect data relevant to the context; for example, investigating supermarket customer complaints that breakfast cereals with the most sugar are positioned at children’s eye level, discussing what questions they would need to ask and answer

  VC2M4ST03 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics