4. Descriptive statistics

In this chapter, we delve into the fundamentals of descriptive statistics, a crucial step in data analysis that involves summarising datasets into comprehensible and concise forms. The chapter begins by exploring the rationale behind descriptive statistics and introduces a real-world dataset, afl.margins, derived from the 2010 Australian Football League season. Through practical illustrations using jamovi, readers learn about various measures of central tendency, including the mean, median, and mode, and their respective applications. The chapter highlights how these measures offer insights into the "typical" values within data, while also explaining when and why each measure is appropriate depending on the data scale. Additionally, the text underscores the significance of visual aids like histograms to enhance the interpretability of numerical summaries.

Further, the chapter explores measures of variability, such as range, interquartile range, variance, and standard deviation, each serving to describe the spread or dispersion of data. Detailed explanations and examples clarify their computation, interpretation, and relevance, emphasising practical considerations like robustness to outliers. The discussion extends to skewness and kurtosis, offering insights into asymmetry and tail thickness in data distributions. Readers are also introduced to z-scores, enabling standardised comparisons across variables. The chapter concludes with guidance on calculating descriptive statistics for subgroups and summarises the key concepts. This foundational knowledge sets the stage for the subsequent chapter on data visualisation, equipping readers with essential tools for effective data analysis.