Chapter 6 Statistics

Statistics turns measurements into evidence. Water professionals collect flow, pressure, turbidity, concentration, rainfall, and equipment data, then summarize patterns and judge whether the observations support a practical conclusion. This chapter develops statistics as a full component of the book. It follows the MATH 128 sequence from data matrices and study design through numerical summaries, variability, quartiles, boxplots, outliers, skewness, and the choice of appropriate measures. The central distinction is between describing the data that were observed and making claims that the data-collection method can support. The statistical framework is consistent with the OpenIntro material used in the source notes (Diez, Barr, and Çetinkaya-Rundel 2019).

Learning outcomes. By the end of this chapter, you should be able to:

• identify cases, variables, and variable types in a data matrix;
• distinguish populations, samples, parameters, and statistics;
• recognize sampling bias and compare sampling methods;
• distinguish observational studies from experiments and evaluate design principles;
• calculate and interpret measures of centre and variability;
• construct five-number summaries and identify potential outliers; and
• describe distribution shape and select appropriate numerical summaries.