Univariate Data Overview

Investigating data distributions, including:

• review of types of data

• review of representation, display and description of the distributions of categorical variables: data tables, two-way frequency tables and their associated segmented bar charts

• use of the distribution/s of one or more categorical variables to answer statistical questions

• review of representation, display and description of the distributions of numerical variables: dot plots, stem plots, histograms; the use of a log (base 10) scale to display data ranging over several orders of magnitude and their interpretation in powers of ten

• summary of the distributions of numerical variables; the five-number summary and boxplots (including the use of the lower fence (Q1 – 1.5 × IQR) and upper fence (Q3 + 1.5 × IQR) to identify and display possible outliers); the sample mean and standard deviation and their use in comparing data distributions in terms of centre and spread

• use of the distribution/s of one or more numerical variables to answer statistical questions

• the normal model for bell-shaped distributions and the use of the 68–95–99.7% rule to estimate percentages and to give meaning to the standard deviation; standardised values (z-scores) and their use in comparing data values across distributions

• population and sample, random numbers and their use to draw simple random samples from a population or randomly allocate subjects to groups, the difference between population parameters (e.g., µ and σ), sample statistics (e.g., x and s).

Assessment Tasks Overview

• Chapter Tests
• Combined SAC (At the end of Chapter 6)

Learning Goals/Success Criteria

Chapter 1 Displaying and describing Data Distributions

Chapter 2 Summarizing Numerical Data