Descriptive Statistics

Descriptive statistics are the methods used to summarise and present the features of a dataset without generalising beyond it. They condense a collection of observations into a few interpretable numbers and pictures, describing where the data are centred, how much they vary, and what shape their distribution takes.

Definition

Descriptive statistics are numerical and graphical summaries that characterise the central tendency, variability, and distribution of the data in hand, describing the sample itself rather than inferring properties of a larger population.

Scope

This entry covers what descriptive statistics are, how they differ from inferential statistics, and the main families of descriptive measure: counts and proportions for categorical data, and location and spread for numerical data. It is a methodological reference and does not give clinical guidance.

Core questions

• What kind of variable is being summarised, and which descriptive measure suits it?
• Where do the data centre, and how widely do they spread?
• How should a categorical variable be summarised compared with a continuous one?

Key concepts

• Descriptive versus inferential statistics
• Frequencies, counts, and proportions for categorical data
• Measures of central tendency
• Measures of dispersion
• Tabular and graphical summary
• Levels of measurement (nominal, ordinal, interval, ratio)

Mechanisms

Descriptive analysis begins by classifying each variable by its measurement level. Categorical variables are summarised with counts, proportions, and frequency tables; numerical variables are summarised with a measure of central tendency paired with a measure of dispersion, chosen according to the distribution's shape — the mean with the standard deviation for roughly symmetric data, and the median with the interquartile range for skewed data. These numerical summaries are commonly accompanied by graphical displays so that distributional features the numbers cannot convey become visible.

Clinical relevance

Descriptive statistics populate the baseline characteristics tables and results sections of virtually all clinical studies, so interpreting them is essential to reading the medical literature. This entry describes how data are summarised for appraisal and is not a basis for individual diagnostic or treatment decisions.

Epidemiology

In epidemiologic and clinical research, descriptive statistics are the first analytic output, used to characterise study samples, exposures, and outcomes before any association or effect is estimated. Transparent reporting of descriptive measures is a basic expectation of study reporting standards.

History

Descriptive summarisation predates formal statistical inference, growing out of demographic and actuarial record-keeping. The twentieth century separated the descriptive and inferential roles of statistics conceptually, and John Tukey's exploratory data analysis programme later re-emphasised description and visual summary as a distinct and important phase of analysis.

Key figures

• John W. Tukey
• Douglas G. Altman

Seminal works

• tukey-1977
• gupta-2019

Frequently asked questions

How do descriptive statistics differ from inferential statistics?

Descriptive statistics summarise the data that were collected; inferential statistics use those data to make probabilistic statements about a broader population. Descriptive measures make no claim beyond the observed sample.

Which descriptive measures should be reported for a continuous variable?

A measure of central tendency together with a measure of spread, chosen to match the distribution: mean and standard deviation when the data are approximately symmetric, median and interquartile range when they are skewed.