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• 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

• VCMSP268

  Identify and investigate issues involving numerical data collected from primary and secondary sources

  Elaborations

  • obtaining secondary data from newspapers, the Internet and the Australian Bureau of Statistics
  • investigating secondary data relating to the distribution and use of non-renewable resources around the world

  VCMSP268 | Mathematics | Level 7 | 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

• VCMSP371

  Investigate reports of studies in digital media and elsewhere for information on their planning and implementation

  Elaborations

  • evaluating the appropriateness of sampling methods in reports where statements about a population are based on a sample
  • evaluating whether graphs in a report could mislead, and whether graphs and numerical information support the claims

  VCMSP371 | Mathematics | Level 10A | Statistics and Probability | Chance

• VCMSP373

  Use digital technology to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation, make predictions based on this straight line and discuss limitations

  Elaborations

  • investigating different techniques for finding a ‘line of best fit’
  • using a fitted line to data to make predictions between and beyond existing data value sand discuss limitations of these predictions

  VCMSP373 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• 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

• VCMSP322

  Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'

  Elaborations

  • using Venn diagrams or two-way tables to calculate relative frequencies of events involving ‘and’, ‘or’ questions
  • using relative frequencies to find an estimate of probabilities of ‘and’, ‘or’ events

  VCMSP322 | Mathematics | Level 9 | Statistics and Probability | Chance

• VCMSP321

  List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events

  Elaborations

  • conducting two-step chance experiments
  • using systematic methods to list outcomes of experiments and to list outcomes favourable to an event
  • comparing experiments which differ only by being undertaken with replacement or without replacement

  VCMSP321 | Mathematics | Level 9 | Statistics and Probability | Chance

• VCMSP353

  Investigate and describe bivariate numerical data, including where the independent variable is time

  Elaborations

  • investigating biodiversity changes in Australia since European occupation
  • constructing and interpreting data displays representing bivariate data over time
  • constructing scatter-plots for two numerical variables and investigate trends such as water storage levels over time or weight and height distributions

  VCMSP353 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP348

  Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements
  • using arrays and tree diagrams to determine probabilities

  VCMSP348 | Mathematics | Level 10 | Statistics and Probability | Chance

• VCMSP324

  Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources

  Elaborations

  • comparing the annual rainfall in various parts of Australia, Pakistan, New Guinea and Malaysia

  VCMSP324 | Mathematics | Level 9 | Statistics and Probability | Data representation and interpretation

• VCMSP347

  Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence

  Elaborations

  • recognising that an event can be dependent on another event and that this will affect the way its probability is calculated

  VCMSP347 | Mathematics | Level 10 | Statistics and Probability | Chance

• VCMSP352

  Use scatter plots to investigate and comment on relationships between two numerical variables

  Elaborations

  • using authentic data to construct scatter plots, make comparisons and draw conclusions

  VCMSP352 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP350

  Construct and interpret box plots and use them to compare data sets

  Elaborations

  • understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
  • using parallel box plots to compare data about the age distribution of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

  VCMSP350 | Mathematics | Level 10 | 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

• VCMSP351

  Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data

  Elaborations

  • investigating data in different ways to make comparisons and draw conclusions
  • using a dot plot, box-plot or histogram to construct a cumulative frequency distribution for a set of data

  VCMSP351 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP349

  Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range

  Elaborations

  • finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the box plot, 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

  VCMSP349 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP354

  Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data

  Elaborations

  • investigating the use of statistics in reports regarding the growth of Australia's trade with other countries of the Asia region
  • evaluating statistical reports comparing the life expectancy of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

  VCMSP354 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP297

  Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the differences between convenience, judgemental and simple random sampling from a population

  VCMSP297 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• 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