The statistician who planned India: P.C. Mahalanobis

Anagha Telang

An Indian Scientist and an applied statistician, P.C. Mahalanobis is popularly rememberd for the Mahalanobis distance, a statistical measure, and for being one of the members of the first Planning Commission of free India. 

Born on 29 June, 1893 in a Bengali family at Calcutta during the British rule, his full name was Prasanta Chandra Mahalanobis.  Mahalanobis did his schooling from the Brahmo Boys School in Calcutta, graduating in 1908. He joined the Presidency College, Calcutta where he was taught by famous personalities like,  Jagadish Chandra Bose, and Prafulla Chandra Ray. Others attending were Meghnad Saha, a year junior, and Subhas Chandra Bose, two years his junior at college. In 1912 Mahalanobis received a Bachelor of Science degree with honours in physics. Later he left for England in 1913 to join the University of London.

He missed a train and stayed with a friend at King's College, Cambridge. He was impressed by King's College Chapel and his host's friend M. A. Candeth who later suggested that P.C. could try joining there, which he did. He was a good student at King's, but also took an interest in cross-country walking and punting on the river. He started interacting  with the mathematical genius Srinivasa Ramanujan during the latter's time at Cambridge. After his Tripos in physics, Mahalanobis worked with C. T. R. Wilson at the Cavendish Laboratory. He took a short break and came back to India, where he was introduced to the Principal of Presidency College and was invited to take classes in physics.

After returning back to England, Mahalanobis was introduced to the journal Biometrika. This interested him so much that he bought a complete set and took them to India. He discovered the utility of statistics to problems in meteorology and anthropology and started working on problems on his journey back to India.

Later, In Calcutta, Mahalanobis met Nirmalkumari, daughter of Herambhachandra Maitra, a leading educationist and member of the Brahmo Samaj. They married on 27 February 1923.

Indian Statistical Institute...
Many of  Mahalanobis colleagues took interest in statistics. An informal group developed in the Statistical Laboratory, which was located in his room at the Presidency College, Calcutta. Mahalanobis called a meeting with Pramatha Nath Banerji (Minto Professor of Economics), Nikhil Ranjan Sen (Khaira Professor of Applied Mathematics) and Sir R. N. Mukherji  On 17 December 1931 and together they established the Indian Statistical Institute (ISI), and formally registered on 28 April 1932 as a non-profit distributing learned society under the Societies Registration Act XXI of 1860.

Initially the institute was in the Physics Department of the Presidency College; its expenditure in the first year was Rs. 238 and it gradually grew with the pioneering work of a group of his colleagues, including S. S. Bose, J. M. Sengupta, R. C. Bose, S. N. Roy, K. R. Nair, R. R. Bahadur, Gopinath Kallianpur, D. B. Lahiri and C. R. Rao. Through Pitamber Pant, who was a secretary to Prime Minister Jawaharlal Nehru the institute gained major assistance . Pant was trained in statistics at the Institute and took a keen interest in its affairs.

In 1933, the Institute founded the journal Sankhya, along the lines of Karl Pearson's Biometrika.

Later, the institute started a training section in 1938. Many of the early workers left the ISI for careers in the United States and with the government of India. Mahalanobis then invited J. B. S. Haldane to join him at the ISI. Haldane joined as a Research Professor from August 1957, staying until February 1961. He resigned from the ISI due to frustrations with the administration and disagreements with Mahalanobis' policies.

In 1959, the institute was declared as an institute of national importance and a deemed university.

Contributions to statistics...

Mahalanobis distance

  • PC got a chance to meet Nelson Annandale,The director of the Zoological Survey of India, at the 1920 Nagpur session of the Indian Science Congress where Annandale asked him to analyse anthropometric measurements of Anglo-Indians in Calcutta.  
  • Mahalanobis had been influenced by the anthropometric studies published in the journal Biometrika and he chose to ask the questions on what factors influence the formation of European and Indian marriages. 
  • He wanted to examine if the Indian side came from any specific castes. He used the data collected by Annandale and the caste specific measurements made by Herbert Risley to come up with the conclusion that the sample represented a mix of Europeans mainly with people from Bengal and Punjab but not with those from the Northwest Frontier Provinces or from Chhota Nagpur. 
  • He also concluded that the intermixture more frequently involved the higher castes than the lower ones. 
  • This analysis was described by his first scientific paper in 1922. During the course of these studies he found a way of comparing and grouping populations using a multivariate distance measure. 
  • This measure, denoted "D2" and now eponymously named Mahalanobis distance, is independent of measurement scale. Mahalanobis also took an interest in physical anthropology and in the accurate measurement of skull measurements for which he developed an instrument that he called the "profiloscope".

Sample surveys
  • His most important contributions are related to large-scale sample surveys. He introduced the concept of pilot surveys and advocated the usefulness of sampling methods. 
  • Early surveys began between 1937 and 1944 and included topics such as consumer expenditure, tea-drinking habits, public opinion, crop acreage and plant disease.
  • He introduced a method for estimating crop yields which involved statisticians sampling in the fields by cutting crops in a circle of diameter 4 feet. Others such as P. V. Sukhatme and V. G. Panse who began to work on crop surveys with the Indian Council of Agricultural Research and the Indian Agricultural Statistics Research Institute suggested that a survey system should make use of the existing administrative framework. 
  • The differences in opinion led to acrimony and there was little interaction between Mahalanobis and agricultural research in later years.

Seccond Five year plan (1956-1961)
  • The Second five year Plan of India was particularly in the development of the public sector and "rapid Industrialisation". The plan followed the Mahalanobis model, an economic development model developed by P.C. in 1953. 
  • The plan attempted to determine the optimal allocation of investment between productive sectors in order to maximise long-run economic growth. It used the prevalent state of art techniques of operations research and optimization as well as the novel applications of statistical models developed at the Indian Statistical Institute. 
  • The plan assumed a closed economy in which the main trading activity would be centred on importing capital goods.

Mahalanobis also had an abiding interest in cultural pursuits and served as secretary to Rabindranath Tagore, particularly during the latter's foreign travels, and also worked at his Visva-Bharati University, for some time.

Awards & Honours...
  • Fellow of the Indian Academy of Sciences (FASc, 1935)
  • Fellow of the Indian National Science Academy (FNA, 1935)
  • Officer of the Order of the British Empire (Civil Division), 1942 New Year Honours list
  • Weldon Memorial Prize from the University of Oxford (1944)
  • Fellow of the Royal Society, London (1945)[1]
  • President of Indian Science Congress (1950)
  • Fellow of the Econometric Society, USA (1951)
  • Fellow of the Pakistan Statistical Association (1952)
  • Honorary Fellow of the Royal Statistical Society, UK (1954)
  • Sir Deviprasad Sarvadhikari Gold Medal (1957)
  • Foreign member of the Academy of Sciences of the USSR (1958)
  • Honorary Fellow of King's College, Cambridge (1959)
  • Fellow of the American Statistical Association (1961)
  • Durgaprasad Khaitan Gold Medal (1961)
  • Padma Vibhushan (1968)
  • Srinivasa Ramanujan Gold Medal (1968)
  • The government of India decided in 2006 to celebrate his birthday, 29 June, as National Statistical Day.
  • Mahalanobis appears in the 2015 movie The Man Who Knew Infinity about the life of Srinivasa Ramanujan. He is portrayed by Shazad Latif.

P.C. Mahalanobis died on 28 June 1972, a day before his seventy-ninth birthday. Till his death, he was active doing research work and discharging his duties as the Secretary and Director of the Indian Statistical Institute and as the Honorary Statistical Advisor to the Cabinet of the Government of India.

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