Descriptive Statistics

Definition

Descriptive statistics are numerical and graphical summaries that characterise the basic features of a dataset. They include measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation, range, interquartile range), and graphical displays (histograms, box plots, bar charts).

Why It Matters

Before conducting any inferential analysis, researchers must understand the shape, centre, and spread of their data. Descriptive statistics reveal outliers, skewness, missing patterns, and distributional anomalies that could invalidate subsequent modelling. They also provide the foundation for communicating results to audiences who may not have statistical training.

Example

A researcher collects data on 200 patients' blood pressure. Before running a regression, she examines descriptive statistics: the mean is 135 mmHg, the median is 132 mmHg, and the standard deviation is 18 mmHg. A histogram reveals a slight right skew, and a box plot flags five outliers above 180 mmHg. She decides to report both mean and median, and to run the regression both with and without the outliers to assess sensitivity.

Related Terms

• Mean
• Median
• Mode
• Standard Deviation
• Variance
• Skewness
• Outlier
• Inferential Statistics

Software Notes

• SPSS: Analyze > Descriptive Statistics > Frequencies, Descriptives, or Explore. Graphs > Chart Builder produces histograms, box plots, and bar charts.
• R: summary(x) for five-number summary. psych::describe(df) for comprehensive descriptives. hist(x), boxplot(x), and ggplot2::ggplot() for graphics.
• Stata: summarize varname, detail for numerical summaries. tabulate varname for frequency tables. histogram x, graph box x, and graph bar x for graphics.