NSW Syllabuses

# Mathematics K–10 - Stage 4 - Statistics and Probability Data Collection and Representation

## Outcomes

#### A student:

• MA4-1WM

communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

• MA4-3WM

recognises and explains mathematical relationships using reasoning

• MA4-19SP

collects, represents and interprets single sets of data, using appropriate statistical displays

Related Life Skills outcomes: MALS-35SP, MALS-36SP, MALS-37SP

• Students:
• Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)
• define 'variable' in the context of statistics as something measurable or observable that is expected to change over time or between individual observations
• recognise variables as categorical or numerical (either discrete or continuous)
• identify examples of categorical variables (eg colour, gender), discrete numerical variables (eg number of students, shoe size) and continuous numerical variables (eg height, weight) (Communicating)
• recognise that data collected on a rating scale (Likert-type scale) is categorical, eg 1 = dislike, 2 = neutral, 3 = like (Communicating)
• recognise and explain the difference between a 'population' and a 'sample' selected from a population when collecting data
• investigate and determine the differences between collecting data by observation, census and sampling
• identify examples of variables for which data could be collected by observation, eg direction travelled by vehicles arriving at an intersection, native animals in a local area (Communicating)
• identify examples of variables for which data could be collected by a census or by a sample, eg a census to collect data about the income of Australians, a sample for TV ratings (Communicating)
• discuss the practicalities of collecting data through a census compared to a sample, including limitations due to population size, eg in countries such as China and India, a census is conducted only once per decade (Communicating, Reasoning)
• Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (ACMSP206)
• collect data using a random process, eg numbers from a page in a phone book, or from a random number generator
• identify issues that may make it difficult to obtain representative data from either primary or secondary sources
• discuss constraints that may limit the collection of data or result in unreliable data, eg lack of proximity to the location where data could be collected, lack of access to digital technologies, or cultural sensitivities that may influence the results (Communicating, Reasoning)
• investigate and question the selection of data used to support a particular viewpoint, eg the selective use of data in product advertising
• Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169)
• identify the difference between data collected from primary and secondary sources, eg data collected in the classroom compared with data drawn from a media source
• explore issues involved in constructing and conducting surveys, such as sample size, bias, type of data required, and ethics
• discuss the effect of different sample sizes (Communicating, Reasoning)
• describe, in practical terms, how a random sample may be selected in order to collect data about a matter of interest (Communicating, Problem Solving)
• detect and discuss bias, if any, in the selection of a sample (Communicating, Reasoning)
• construct appropriate survey questions and a related recording sheet in order to collect both numerical and categorical data about a matter of interest
• construct a recording sheet that allows efficient collection of the different types of data expected (Communicating, Problem Solving)
• refine questions in a survey after trialling the survey (Communicating)
• decide whether a census or a sample is more appropriate to collect the data required to investigate the matter of interest (Problem Solving)
• collect and interpret information from secondary sources, presented as tables and/or graphs, about a matter of interest, eg sporting data, information about the relationship between wealth or education and the health of populations of different countries
• interpret and use scales on graphs, including those where abbreviated measurements are used, eg '50' on a vertical axis representing thousands is interpreted as '50 000' (Reasoning)
• analyse a variety of data displays used in the print or digital media and in other school subject areas, eg share-movement graphs, data displays showing sustainable food production (Problem Solving)
• identify features on graphical displays that may mislead and result in incorrect interpretation, eg displaced zeros, the absence of labelling on one or both axes, potentially misleading units of measurement (Communicating, Reasoning)
• use spreadsheets or statistical software packages to tabulate and graph data
• discuss ethical issues that may arise from collecting and representing data (Reasoning)
• select and use appropriate scales and labels on horizontal and vertical axes (Communicating, Problem Solving, Reasoning)
• recognise why a half-column-width space is necessary between the vertical axis and the first column of a histogram (Reasoning)
• construct dot plots
• explain the importance of aligning data points when constructing dot plots (Communicating, Reasoning)
• construct ordered stem-and-leaf plots, including stem-and-leaf plots with two-digit stems
• explain the importance of ordering and aligning data values when constructing stem-and-leaf plots (Communicating, Reasoning)
• construct divided bar graphs, sector graphs and line graphs, with and without the use of digital technologies
• calculate the length of bar required for each section of divided bar graphs and the angle at the centre required for each sector of sector graphs (Problem Solving)
• interpret a variety of graphs, including dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphs
• calculate the percentage of the whole represented by different categories in a divided bar graph or sector graph (Problem Solving)
• compare the strengths and weaknesses of different forms of data display (Reasoning)
• identify and explain which graph types are suitable for the type of data being considered, eg sector graphs and divided bar graphs are suitable for categorical data, but not for numerical data (Communicating, Reasoning)
• draw conclusions from data displayed in a graph, eg 'The graph shows that the majority of Year 8 students who play a musical instrument play a string instrument' (Communicating, Reasoning)

### Background Information

Students in Stage 4 can be expected to have some prior knowledge of both dot plots and line graphs, as these types of graph are introduced in Stage 3. They construct, describe and interpret column graphs in Stage 2 and Stage 3; however, histograms, divided bar graphs and sector graphs (pie charts) are not encountered until Stage 4.

Statistical data is part of everyday life. Data may be displayed in tables or graphs, and may appear in all types of media. Graphs provide a visual overview of the substrand under investigation. Students should be aware that while many graphs are accurate and informative, some can be misleading. They need to experience interpreting a wide variety of graphical representations, including column graphs, dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphs. Students should be able to select an appropriate graph to represent the collected data.

#### Purpose/Relevance of Substrand

In investigations, it is important to develop knowledge and understanding of the ways in which relevant and sufficient data can be collected, as well as the associated implications and limitations. It is also important to develop knowledge and understanding of what constitute appropriate sources of data, both primary and secondary. Data and statistics are used in many aspects of our everyday and working lives. Data is collected to provide information on many topics of interest and to assist in making decisions regarding important issues (eg projects aimed at improving or developing products or services). Users at all levels need to have skills in the organisation and display of the collected data for its interpretation and analysis. This can be achieved in a wide variety of ways, including through the use of frequency distribution tables and simple data displays/graphs, such as frequency histograms and polygons, dot plots, stem-and-leaf plots, divided bar graphs, sector graphs and line graphs.

### Language

In everyday language, the term 'pie chart' is often used in reference to sector graphs.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA4‑19MG the sub-elements (and levels) of Operating with percentages (OwP2) and Interpreting and representing data (IRD3-IRD6) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.