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

## Content

• 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