YEAR 8 MATHS FOCUS
STATISTICS AND PROBABILITY
SINGLE VARIABLE DATA ANALYSIS
OUTCOME
A student:
MA420SP:
analyses single sets of data using measures of location, and range
TEACHING POINTS  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. 
RELEVANCE  Singlevariable (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 singlevariable 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. Singlevariable 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. 
Expectations of Attainment
Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data (ACMSP171) 

determine the median, mode and range for sets of data
 
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 shoesize 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 outlierCritical and creative thinking
 
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)  calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including frequencydistribution tables, frequency histograms, stemandleaf plots and dot plots 
draw conclusions based on the analysis of data displays using the mean, median and/or mode, and range 
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)

Construct and compare a range of data displays, including stemandleaf plots and dot plots (ACMSP170)  use a tally to organise data into a frequency distribution table 
construct and interpret frequency histograms and polygons
 
construct dot plots
 
construct ordered stemandleaf plots, including stemandleaf plots with twodigit stems
 
construct divided bar graphs, sector graphs and line graphs, with and without the use of digital technologiesLiteracy
 
interpret a variety of graphs, including dot plots, stemandleaf plots, divided bar graphs, sector graphs and line graphsLiteracy

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