NSW Syllabuses

# Mathematics K–10 - Stage 5.1 - Statistics and Probability Single Variable Data Analysis

## Outcomes

#### A student:

• MA5.1-1WM

uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-2WM

selects and uses appropriate strategies to solve problems

• MA5.1-3WM

provides reasoning to support conclusions that are appropriate to the context

• MA5.1-12SP

uses statistical displays to compare sets of data, and evaluates statistical claims made in the media

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

## Content

• identify and investigate relevant issues involving at least one numerical and at least one categorical variable using information gained from secondary sources, eg the number of hours in a working week for different professions in Australia, the annual rainfall in various parts of Australia compared with that of other countries in the Asia–Pacific region
• construct frequency histograms and polygons from a frequency distribution table
• use the terms 'positively skewed', 'negatively skewed', 'symmetric' or 'bi-modal' to describe the shape of distributions of data
• describe the shape of data displayed in stem-and-leaf plotsdot plots and histograms (Communicating)
• suggest possible reasons why the distribution of a set of data may be symmetric, skewed or bi-modal (Reasoning)
• construct back-to-back stem-and-leaf plots to display and compare two like sets of numerical data, eg points scored by two sports teams in each game of the season
• describe differences in the shapes of the distributions of two sets of like data (Communicating)
• interpret two sets of numerical data displayed in back-to-back stem-and-leaf plots, parallel dot plots and histograms
• calculate and compare means, medians and ranges of two sets of numerical data displayed in back-to-back stem-and-leaf plots, parallel dot plots and histograms
• make comparisons between two like sets of data by referring to the mean, median and/or range, eg 'The range of the number of goals scored in the various weeks of a competition for Team A is smaller than that for Team B, suggesting that Team A is more consistent from week to week than Team B' (Communicating, Reasoning)
• Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253)
• interpret media reports and advertising that quote various statistics, eg media ratings, house prices, sports results, environmental data
• analyse graphical displays to recognise features that may have been manipulated to cause a misleading interpretation and/or support a particular point of view
• explain and evaluate the effect of misleading features on graphical displays (Communicating, Reasoning)
• critically review claims linked to data displays in the media and elsewhere
• suggest reasons why data in a display may be misrepresented in the accompanying text (Communicating, Reasoning)
• consider, informally, the reliability of conclusions from statistical investigations, taking into account issues such as factors that may have masked the results, the accuracy of measurements taken, and whether the results can be generalised to other situations

### Background Information

In Stage 5.1, students are only required to recognise the general shape and lack of symmetry in skewed distributions. No specific analysis of the relative positions of mean, median and mode is required.

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

When working towards the outcome MA5.1-12SP the sub-elements (and levels) of Interpreting and representing data (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.