NSW Syllabuses

# Mathematics K–10 - Stage 4 - Statistics and Probability Single Variable Data Analysis

## Outcomes

#### A student:

• MA4-1WM

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

• MA4-2WM

applies appropriate mathematical techniques to solve problems

• MA4-3WM

recognises and explains mathematical relationships using reasoning

• MA4-20SP

analyses single sets of data using measures of location, and range

• Students:
• Calculate mean, medianmode and range for sets of data and interpret these statistics in the context of data (ACMSP171)
• calculate the mean, $$\bar x$$, of a set of data using $$\bar x = \dfrac{\text{sum of data values}}{\text{number of data values}}$$
• recognise that the mean is often referred to as the 'average' in everyday language (Communicating)
• use the statistical functions of a calculator to determine the mean for small sets of data (Problem Solving)
• use the statistical functions of a spreadsheet to determine the mean for large sets of data (Problem Solving)
• determine the median, mode and range for sets of data
• recognise which statistical measures are appropriate for the data type, eg the mean, median and range are meaningless for categorical data (Reasoning)
• use the statistical functions of a spreadsheet to determine the median, mode and range for large sets of data (Communicating, Problem Solving)
• identify and describe the mean, median and mode as 'measures of location' or 'measures of centre', and the range as a 'measure of spread'
• describe, in practical terms, the meaning of the mean, median, mode and/or range in the context of the data, eg when referring to the mode of shoe-size data: 'The most popular shoe size is size 7'
• Investigate the effect of individual data values, including outliers, on the mean and median (ACMSP207)
• identify any clusters, gaps and outliers in sets of data
• investigate the effect of outliers on the mean, median, mode and range by considering a small set of data and calculating each measure, with and without the inclusion of an outlier
• explain why it is more appropriate to use the median than the mean when the data contains one or more outliers (Communicating, Reasoning)
• determine situations when it is more appropriate to use the median or mode, rather than the mean, when analysing data, eg median for property prices, mode for shoe sizes (Reasoning)
• analyse collected data to identify any obvious errors and justify the inclusion of any individual data values that differ markedly from the rest of the data collected
• Describe and interpret data displays using mean, median and range (ACMSP172)
• Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293)
• investigate ways in which different random samples may be drawn from the same population, eg random samples from a census may be chosen by gender, postcode, state, etc
• calculate and compare summary statistics (mean, median, mode and range) of at least three different random samples drawn from the same population
• use a spreadsheet to calculate and compare summary statistics of different random samples drawn from the same population (Communicating, Problem Solving)
• recognise that summary statistics may vary from sample to sample (Communicating)
• recognise that the way in which random samples are chosen may result in significant differences between their respective summary statistics, eg a random sample of girls compared to a random sample of boys from the population, random samples chosen by postcode (Communicating, Reasoning)
• suggest reasons why different random samples drawn from the same population may have different summary statistics (Communicating, Reasoning)

### Background Information

Many opportunities occur in this substrand for students to strengthen their skills in: collecting, analysing and organising information; communicating ideas and information; planning and organising activities; working with others and in teams; using mathematical ideas and techniques; using technology, including spreadsheets.

#### Purpose/Relevance of Substrand

Single-variable (or 'univariate') data analysis involves the statistical examination of a particular 'variable' (ie a value or characteristic that changes for different individuals, etc) and is of fundamental importance in the statistics used widely in everyday situations and in fields including education, business, economics and government. Most single-variable data analysis methods are used for descriptive purposes. In organising and displaying the data collected, frequencies, tables and a variety of data displays/graphs are used. These data displays/graphs, and numerical summary measures, are used to analyse and describe a data set in relation to a single variable, such as the scores on a test, and to compare a data set to other data sets. Single-variable data analysis is commonly used in the first stages of investigations, research, etc to describe and compare data sets, before being supplemented by more advanced 'bivariate' or 'multivariate' data analysis.

### Language

The term 'average', when used in everyday language, generally refers to the mean and describes a 'typical value' within a set of data.

Students need to be provided with opportunities to discuss what information can be drawn from the data presented. They need to think about the meaning of the information and to put it into their own words.

Language to be developed would include superlatives, comparatives, expressions such as 'prefer … over', etc.

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

When working towards the outcome MA4‑20MG the sub-elements (and levels) of Interpreting and representing data (IRD4-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.