Prasanta Chandra Mahalanobis, or PCM as he was known, was an Indian Statistician responsible for developing the Indian Statistical System and for establishing the internationally renowned Indian Statistical Institute (ISI).
PCM was born on June 29, 1893 and died on June 28, 1972 at the age of 78, a day before his 79th birthday. He had his early education in the Brahmo Boys School and received his BSc degree in Physics in 1912 from the Presidency College in Calcutta. He went to England the next year for higher studies. A contemporary of the great Indian mathematician Srinivasa Ramanujan, PCM received tripos in Physics from King’s College, London, in 1915. He returned to India and joined the Indian Education Service in 1915 as Professor of Physics at the Presidency College, Calcutta.
Struck by Statistics
Soon, PCM went back to England but his return to India got delayed due to the World War I. It is said that while browsing in the library of King’s College, his tutor Macaulay drew his attention to volumes of the journal Biometrika, edited by Karl Pearson, which contained statistical tables relating to area under curves among others. He got so interested in the contents and the new science of Statistics that he bought a complete set of Biometrika volumes to read on the boat trip back to India. He continued to understand the new discipline and its applications in Physics and other areas relating to measurement after returning to Calcutta.
In a letter dated 1935, PCM acknowledges C W Peake, Principal, Presidency College as the man who introduced him to Biometrika tables and other technical aspects of statistical ideas. Thus both Macaulay and Peake were instrumental in introducing PCM to the subject of Statistics. Acharya Brajendranath Seal, Professor of Philosophy at the Calcutta University during 1912-21, who appreciated this new subject, asked PCM to analyse examination results of Calcutta university, passing on some of his own calculations. PCM attributed his background of statistical knowledge, its logical aspects and practical side of applications to Seal.
Remedy for Floods, Courtesy Statistics
In 1920, PCM had a chance meeting with N. Annandale, the then Director of Zoological Survey of India, who had taken anthropometric measurements on Anglo-Indians of Calcutta. In the year 1922, a disastrous flood occurred in North Bengal. An expert committee of engineers appointed by the government recommended the construction of expensive retarding basins to hold up the flood waters. PCM, on a statistical analysis of rainfall and floods over a period of 50 years, suggested a less expensive remedy of rapid drainage and not holding up flood waters. This was implemented and proved effective.
A similar problem of flood control in Orissa was investigated by him in the year 1926. This detailed analysis on flood research resulted in the starting of the construction of Hirakud dam, a multipurpose hydroelectricity project, in the year 1947, which was completed in 1957. PCM’s early work on river floods is related to what is now known as Operations Research (OR) which gained importance in defence studies as separate discipline after the second World War.
PCM discovered the utility of Statistics and Statistical methods in studying the problems of meteorology and anthropology. Many colleagues of PCM at the Presidency College took interest in Statistics and they established and registered the Indian Statistical Institute (ISI) on April 28, 1932 as a non-profit society. Initially located in the Department of Physics of the Presidency College, the institute later moved to its present location, Baranagar in Calcutta. The institute founded the journal Sankhya in 1933 and PCM was its editor until his demise. ISI was declared as an institute of national importance in 1959. I was among the first batch of students admitted into ISI’s Master’s (M Stat) program in 1960 and attended PCM’s lectures on counting and measurement.
Besides laying the foundations of statistics in India, PCM advocated for an international programme for education in Statistics, especially in those countries that did not possess potential resources of trained personnel. The International Statistical Education Centre (ISEC) was started in 1950, jointly operated by ISI and the government of India and located in the ISI campus.
The Mahalanobis Distance
PCM made important contributions to statistical methods for data analysis. He introduced a distance concept in Statistics now known as the Mahalanobis distance. It is one of the most widely used metrics to measure distances between groups or populations based on measurements in multiple dimensions. It is used for cluster analysis as well as classification in Big Data problems now. PCM proposed this distance in 1930 and it is denoted by D2 in statistical literature. This distance does not depend on the scale of measurement.
Mahalanobis distance is not just only a fundamental contribution to the classification problems in general and taxonomic classification in particular, but also plays an important role in Machine Learning and Pattern Recognition, Big Data of the present day. This concept was also used by Taguchi for developing diagnostic measurement systems which are now known as Mahalanobis Taguchi Systems (MTS).
Sample Surveys
Another important contribution of PCM was the idea of large scale sample surveys. He also introduced the concept of pilot surveys and suggested sampling methods for surveys to study subjects such as consumer expenditure, crop acreage, and prevalence of plant disease for the first time in the world. According to the world renowned statistician R.A. Fisher, “The ISI has taken the lead in the original development of the techniques of sample surveys, the most potent fact-finding process available to the administration”.
PCM conducted large scale sample surveys between July 1944 and February 1945 to assess the extent of the disaster of the Bengal Famine, including the number of people affected. The planning, preparation and findings of the survey were presented in an article in journals Sankhya and Asiatic Review in 1946.
Starting from the first large sample survey in the whole world for jute forecast in 1934, PCM had developed a strong and trustworthy statistical heritage in India through tireless efforts. He considered large scale surveys a key branch of Statistics. He was instrumental in establishing the National Sample Survey (NSS) organisation in 1950 and the Central Statistical Organisation (CSO) in 1951.
Mahalanobis introduced the technique of interpenetrating subsamples to check data accuracy in his surveys by cross-checking by an independent set of investigators for data collection. The desire to have built-in cross checks of errors in sampling led him to introduce the idea of interpenetrating subsamples which is now considered as the precursor for resampling methods like bootstrap in the theory of statistical inference.
PCM was a physicist by training, a statistician by instinct and an economist by conviction. His initial training in Physics might have made him conscious about errors in measurements and observations. He was at times called the Professor of Counting and Measurement, in short PCM, coinciding with his name.
A member of the planning commission appointed by the government of India, he contributed to India’s second five-year plan by emphasising on industrialisation on the basis of what is called two-sector model. PCM was a supporter of technology. He played a crucial role in the campaign to bring the first digital computer to India. ISI procured India’s first computer in 1956 and the second in 1959.
PCM was the Secretary and Director of the Indian Statistical Institute and the Honorary Statistical Adviser to the government of India till his demise. He received the Fellowship of the Royal Society in 1945 based on his work on large scale sample surveys. He was awarded Padma Vibhushan by the government of India in 1968. For his contributions to statistical science and economic planning, PCM received numerous awards from several academic organisations in India and abroad. He was an institution builder. Indian Statistical Institute is a mighty monument of his handicraft. It is said “not armies, not nations advance the race; but here and there, in the course of ages, an individual stood up and cast his shadow on the world”. This is true of Professor Prasanta Chandra Mahalanobis.
A Lasting Legacy
During the period 1992-95 when I was the Director of ISI, Indian Council of Social Science Research (ICSSR) supported a project leading to the book, Prasanta Chandra Mahalanobis: A biography, by Ashok Rudra. It was published in 1996 by the ISI and the Oxford University Press.
PCM’s birthday is observed every year as the National Statistics Day. In his honour, the Ministry of Statistics and Programme Implementation (MoSPI) of the government of India had instituted the Mahalanobis Prize, presented once in two years. In addition, a new award in his memory was instituted last year by the MoSPI for outstanding contributions to the subject of Official Statistics in India. The first recipient of this award was Dr C Rangarajan, former Governor of the Reserve Bank of India.
