selects appropriate notations and conventions to communicate mathematical ideas and solutions
constructs arguments to prove and justify results
uses quartiles and box plots to compare sets of data, and evaluates sources of data
Related Life Skills outcomes: MALS-35SP, MALS-36SP, MALS-37SP
- determine the upper and lower extremes, median, and upper and lower quartiles for sets of numerical data, ie a 'five-number summary'
- describe the proportion of data values contained between various quartiles, eg 75% of data values lie between the lower quartile and the upper extreme (Communicating, Reasoning)
- determine the interquartile range for sets of data
- recognise that the interquartile range is a measure of spread of the middle 50% of the data (Reasoning)
- compare the relative merits of the range and the interquartile range as measures of spread
- explain whether the range or the interquartile range is a better measure of spread for particular sets of data (Communicating, Reasoning)
- Construct and interpret box plots and use them to compare data sets (ACMSP249)
- construct a box plot using the median, the upper and lower quartiles, and the upper and lower extremes of a set of data
- compare two or more sets of data using parallel box plots drawn on the same scale
- describe similarities and differences between two sets of data displayed in parallel box plots, eg describe differences in spread using interquartile range, and suggest reasons for such differences (Communicating, Reasoning)
- determine quartiles from data displayed in histograms and dot plots, and use these to draw a box plot to represent the same set of data
- compare the relative merits of a box plot with its corresponding histogram or dot plot (Reasoning)
- identify skewed and symmetrical sets of data displayed in histograms and dot plots, and describe the shape/features of the corresponding box plot for such sets of data
- Investigate reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians (ACMSP227)
- investigate survey data reported in the digital media and elsewhere to critically evaluate the reliability/validity of the source of the data and the usefulness of the data
- describe bias that may exist due to the way in which the data was obtained, eg who instigated and/or funded the research, the types of survey questions asked, the sampling method used (Reasoning)
- make predictions from a sample that may apply to the whole population
- consider the size of the sample when making predictions about the population (Reasoning)
Graphics calculators and other statistical software will display box plots for entered data, but students should be aware that results may not always be the same. This is because the technologies use varying methods for creating the plots, eg some software packages use the mean and standard deviation by default to create a box plot. This syllabus requires students to create box plots using the upper and lower extremes, the median, and the upper and lower quartiles of sets of data.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA5.2-15SP 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.