Measures of Central Tendency and Dispersion

Definition, role & data types

• What they are — Summary (descriptive) statistics condense a set of observations into a few numbers carrying the essential information — a measure of location / central tendency (where the centre of the data lies) plus a measure of spread / dispersion (how widely values scatter about it). Two numbers — a location and a variability measure — are the usual minimum to describe a continuous variable; quoting location without spread is uninformative.
• Why a pharmacologist needs them — They underpin everything downstream: a trial's baseline table, summarising a dose–response or PK parameter (Cmax, AUC, t½, clearance), describing adverse-event rates, and feeding the point estimate ± its precision into confidence intervals and hypothesis tests. The location/spread split is the foundation on which the whole inferential layer is built.
• Two governing axes — The legitimate summary is chosen to match (a) the type of data and (b) the shape of the distribution — these two axes govern the entire topic.

• Scale dictates the summary — Mean and SD are properly used only for quantitative data that are roughly symmetric; ordinal data are best summarised by the median, nominal/binary by proportions. Applying a mean to nominal data is meaningless. Down-converting a continuous variable into categories (BP → hypertensive/normotensive) discards information and is avoided unless clinically justified.