Descriptive Statistics

Descriptive statistics distill complex datasets into comprehensible numerical summaries that quantify key data characteristics. Measures of central tendency identify the 'typical' values around which data congregate—with the mean capturing the arithmetic average (sensitive to outliers), the median revealing the central value (robust against extreme values), and the mode highlighting the most frequent observation (particularly meaningful for categorical data). These different perspectives on 'average' often tell dramatically different stories about the same dataset, revealing whether distributions are symmetric or skewed.

Dispersion metrics quantify data variability and spread—standard deviation measures average distance from the mean (sensitive to outliers), while interquartile range captures the middle 50% of values (resistant to extreme observations). Range provides the simplest measure of spread but can be dramatically influenced by a single anomalous observation. Shape characteristics like skewness (asymmetry) and kurtosis (tailedness) describe distribution form—revealing whether data follows normal bell curves or exhibits more complex patterns with heavy tails or asymmetric concentrations. Together, these statistical measures provide a mathematical fingerprint of the data's distribution—identifying potential modeling challenges like high-leverage outliers, severe skewness requiring transformation, or multi-modal structures suggesting mixed populations that might require separate analysis approaches.