Content:
MA4-DAT-C-01
Classify data as either numerical (discrete or continuous) or categorical (nominal or ordinal) variables
- Define a variable in the context of statistics as any characteristic, number or quantity that can be measured or counted
- Classify and describe variables as numerical or categorical
- Describe a numerical variable as either discrete or continuous
- Describe a categorical variable as nominal or ordinal
- Distinguish between and compare numerical (discrete or continuous) and categorical (nominal or ordinal) variables
Display data using graphical representations relevant to the purpose of the data
- Represent single datasets using graphs, including frequency histograms and polygons, dot plots, stem-and-leaf plots, divided bar graphs, column graphs, line graphs, sector graphs and pictograms, with or without digital tools
- Include sources, titles, labels and scales when displaying data in a graph
- Select the type of graph best suited to represent various single datasets and justify the choice of graph
- Represent a dataset using a statistical infographic and justify the choice of graphical representation used
Interpret data in graphical representations
- Identify and interpret data displayed on graphs
- Identify features of graphical representations to draw conclusions
- Interpret patterns in graphical representations to make predictions
- Explain why a given graphical representation can lead to a misinterpretation of data
MA4-DAT-C-02
Calculate and compare the mean, median, mode and range for simple datasets
- Calculate the mean (\( \overline{x} \))of a set of data using digital tools
- Calculate and describe the mean, median, mode and range of a dataset
- Classify the mean, median and/or mode as measure(s) of centre to represent the average or typical value of a dataset
- Describe and interpret data displays using mean, median and range
- Identify and describe datasets as having no modes (uniform), one mode (unimodal), 2 modes (bimodal) or multiple modes (multimodal)
- Identify the range as a measure of spread to describe variation in a dataset
- Compare simple datasets using the mean, median, mode and range
Interpret the effect individual data points have on measures of centre and range
- Informally identify clusters, gaps and outliers in datasets and give reasons for their occurrence in the context of the data
- Identify and explain the impact of adding or removing data values that are clustered at one end of a dataset on the measures of centre
- Identify and explain the impact of outliers on the measures of centre and range
- Determine and justify the most appropriate measure of centre to summarise the data in its context
Analyse datasets presented in various ways and draw conclusions
- Identify and describe the shape and distribution of a dataset using the terms symmetrical, negatively skewed and positively skewed
- Associate the shape and distribution of a dataset with the relative size of the mean, median and mode using the terms symmetry and skew
- Define a census as a study of every unit, everyone or everything in a population
- Define a sample as a subset of units in a population selected to represent all units in a population of interest
- Draw conclusions and make informed decisions about data gathered using data-collection techniques, including census and sampling, which is then presented in tables, graphs and charts
MA5-DAT-C-01
Examine standard deviation as a measure of spread
- Identify standard deviation as a measure of spread
- Calculate the standard deviation of a small dataset using digital tools
- Compare small datasets using standard deviation
Determine quartiles and interquartile range
- Determine the 5-number summary for sets of numerical data
- Determine the 5-number summary from graphical representations
- Determine the interquartile range (IQR) for datasets
- Compare and explain the relative merits of range and IQR as measures of spread
Represent datasets using box plots and use them to compare datasets
- Represent numerical datasets using a box plot to display the median, upper and lower quartiles, and maximum and minimum values
- Compare 2 or more numerical datasets using parallel box plots drawn on the same scale
- Compare and contrast the centres, spreads and shapes of 2 or more numerical datasets, using box plots and numerical statistics, including the 5-number summary
- Determine quartiles from datasets displayed in histograms and dot plots, and represent these as a box plot
- Identify and describe skewness or symmetry of datasets displayed in histograms, dot plots and box plots
- Interpret box plots to draw conclusions and make inferences about the dataset
