Key Terms & Concepts — UPSC Mains
Mahalanobis Distance
"A statistical measure of the distance between a point and a distribution, accounting for correlations between variables, devised by P.C. Mahalanobis."
The Mahalanobis distance was introduced by Prasanta Chandra Mahalanobis, founder of the Indian Statistical Institute, in 1936. It measures how many standard deviations a point is from the mean of a distribution, but unlike ordinary Euclidean distance, it accounts for correlations between the variables measured and is scale-invariant. Originally devised for anthropometric research comparing skull measurements across population groups, it is now a standard tool in statistics and machine learning for outlier detection, classification and clustering. It is one of several enduring Mahalanobis legacies, alongside his pioneering of large-scale sample surveys (giving rise to the National Sample Survey) and his authorship of the growth model underlying the Second Five Year Plan (1956-61).
Prelims occasionally tests the concept's association with P.C. Mahalanobis and the ISI; useful for Mains answers on India's contributions to statistical science.
- 1 Devised by P.C. Mahalanobis in 1936.
- 2 Measures distance from a distribution's mean, accounting for correlation between variables; scale-invariant.
- 3 Originally developed for anthropometric comparisons; now used for outlier detection, classification and clustering.
- 4 One of several Mahalanobis legacies alongside the National Sample Survey and the Second Five Year Plan growth model.
The Mahalanobis distance, devised by the same P.C. Mahalanobis who founded the Indian Statistical Institute in 1931, illustrates the institute's foundational role in Indian statistical science.
