P. C. Mahalanobis Founded the Indian Statistical Institute on 17 December 1931 and Started the National Sample Survey in 1950, a Survey Programme That Marked 75 Years in 2025

The Indian Statistical Institute began at a public meeting in Calcutta (now Kolkata) on 17 December 1931 and was registered as a society on 28 April 1932, according to the memoir the Indian National Science Academy published after the death of its founder, Prasanta Chandra Mahalanobis. In 1950 he started the National Sample Survey, a continuing countrywide survey whose first round ran from October 1950 to March 1951. In 2025 the Ministry of Statistics and Programme Implementation marked the survey’s 75th year with a commemorative coin, a customised stamp and a series of events.

His birthday, 29 June, is now India’s Statistics Day. The record behind that honour runs from a college library in Cambridge to flood reports, a jute survey in Bengal and a paper in 1936 that gave statistics a measure carrying his name.

A physics graduate and a journal in a library

Mahalanobis was born in Calcutta on 29 June 1893. He took an honours degree in physics at Presidency College in 1912 and went to King’s College, Cambridge, where he sat the mathematics tripos (the Cambridge honours examinations) in 1914 and the physics tripos in 1915. The Indian National Science Academy memoir says he came across the journal Biometrika in the King’s library, liked it enough to buy a complete set and carried the volumes home to India.

The subject he returned to was almost absent. The memoir records that in the first quarter of the twentieth century India had no teaching or research in statistics at its universities, no statistical society and no journal of statistics. He took up a physics post at Presidency College in 1915, and a statistical workshop grew in his room there. It was called the Statistical Laboratory.

The meeting of 17 December 1931 was called over the signatures of Pramatha Nath Banerji, Nikhil Ranjan Sen and Mahalanobis, with Sir R. N. Mukherji in the chair. The Institute’s own annual report for 2022 to 2023 lists the next step: Sankhya, the Indian Journal of Statistics, appeared in 1933 with a foreword by Rabindranath Tagore. Mahalanobis edited it from its first issue, and he was General Secretary of Tagore’s Visva-Bharati from 1921 to 1931 (see Santiniketan).

The distance that came from a request about Anglo-Indians

In 1920, at the Indian Science Congress in Nagpur, Nelson Annandale, then director of the Zoological Survey of India, asked Mahalanobis to analyse body measurements taken from Anglo-Indians in Calcutta. Probal Chaudhuri of the Institute, writing in 2020, says the D-squared statistic came out of that analysis. The memoir dates Mahalanobis’s first scientific paper on the subject to 1922, in the Records of the Indian Museum.

The formal statement came in 1936, in “On the generalised distance in statistics”, Proceedings of the National Institute of Sciences of India, pages 49 to 55, as the memoir’s bibliography lists it. The idea is a way to measure how far apart two groups are on several measurements at once, with the gap scaled by how much those measurements vary and move together. Chaudhuri notes one consequence: for two groups with the same spread, the linear discriminant function Ronald Fisher published in 1936 sorts a new observation into whichever group is nearer in Mahalanobis distance. The memoir adds that the statistic was widely used for classifying populations, and that Mahalanobis himself questioned whether results depended too much on which measurements were chosen.

Floods, a river bed and the first sums for Hirakud

Before the surveys came the rivers. The memoir describes a flood in North Bengal in 1922, when a committee of engineers was about to recommend retarding basins (large holding areas) to hold back flood water. Referred the question, Mahalanobis studied fifty years of rainfall and flood records and concluded that the basins would not control floods. He recommended faster drainage instead, and the memoir says many of his remedies were carried out and worked.

After a severe flood on the Brahmani in Odisha in 1926, engineers believed the river bed had risen and proposed higher embankments. His study of about sixty years of records, the memoir says, showed no change in the bed, and it pointed to dams in the upper reaches. He also gave the first calculations for a multipurpose flood-control, irrigation and power scheme on the Mahanadi, which the memoir says became the basis of the Hirakud project inaugurated about thirty years later, in 1957. Britannica separately credits him with applying statistics to economic planning for flood control.

Jute, a sample and a ten-year argument

In 1937 he worked out how to estimate the area and yield of the jute crop in Bengal by random sampling. The Press Information Bureau feature, written by a deputy director general of the Ministry of Statistics and Programme Implementation in a personal capacity, adds that the estimates were hard to get accepted and that his dispute with the advocates of counting everything lasted more than a decade. It says he eventually showed that sample estimates were often more accurate than complete counts, with small margins of error, delivered faster and at lower cost.

The methods from the surveys of 1937 to 1944 were published in “On large-scale sample surveys” in the Philosophical Transactions of the Royal Society in 1944. The Royal Society’s archive holds the referee’s report by Alexander Aitken, catalogued as 1943. The archive’s summary says Aitken could find no fault in the statistical theory and judged the paper important both theoretically and administratively.

The PIB feature and the memoir name the same three contributions: pilot surveys, optimum survey design and the interpenetrating network of sub-samples. A pilot survey is a small trial run that tells you the costs and the variation before the main survey is designed. The PIB feature says he used the interpenetrating network of sub-samples to assess and control errors outside the sampling itself, the mistakes that creep in while data are collected and processed. Both sources add that the pilot-survey idea was a forerunner of the sequential analysis Abraham Wald developed about ten years later.

The National Sample Survey

The memoir says that in 1949 Mahalanobis became chairman of the Indian National Income Committee and met gaps in the information needed to compute national income. The National Sample Survey was set up in 1950 to fill them. A survey of the after-effects of the Bengal famine of 1943, the memoir adds, had already made him acutely aware of the poverty of the country. The Institute took charge of its technical direction and tabulation that year, and the Central Statistical Unit, with Mahalanobis as honorary statistical adviser to the Cabinet, dated from 1949. Two years later the Central Statistical Organisation was formed to coordinate the government’s statistical work.

The first round, from October 1950 to March 1951, covered 1,833 villages, according to course material on the government education portal cec.nic.in and to the University of Cambridge. Cambridge adds that the sample stood for a population of roughly 360 million people. Urban areas were first included in the third round, from August to November 1951, according to the same course material. Cambridge also records the early criticism that urban areas were over-represented and that surveyors did not know the conditions of remote villages, and says it took years to design a survey that gave an acceptable level of accuracy.

To check the work, Mahalanobis invited outside experts to review it. The PIB feature says the first review committee included R. A. Fisher, M. H. Hansen, T. Kitagawa, A. Linder and F. Yates. It describes their opinion as “not entirely uncritical” but quotes their report as saying that on sample surveys, those outside India “must expect to have more to learn than to teach”. The memoir’s own judgment is that there was no parallel anywhere in the world for a continuing sample survey covering a whole country for official statistics. It also records that he chaired the United Nations Sub-Commission on Sampling from 1947 to 1951, where he argued for sample surveys in less developed countries.

The University of Cambridge feature reports that Chinese officials sent statisticians to Kolkata in the 1950s to learn from his staff, and that the Institute served as a model for the American statistician Gertrude Cox when she organised statistical training in the United States.

An institute that trained its own statisticians

The Institute taught as well as counted. The memoir says postgraduate study of statistics opened at Calcutta University in 1941 under his guidance. Chaudhuri’s article records that C. R. Rao, one of the first five students to take the new Master’s degree there, was offered a job by Mahalanobis and joined the Institute in 1943. The Institute’s annual report lists Rao’s name beside the Cramer-Rao bound and the Rao-Blackwell theorem among its landmark discoveries.

A central Act of 1959 made the Institute an Institution of National Importance able to award its own degrees. The annual report says it designed the first analog computer in India in 1954 and installed the first digital computer in the country, the HEC-2M, in 1955. The memoir lists his honours: the Weldon Medal of Oxford University in 1944, election as a Fellow of the Royal Society in 1945 and the Padma Vibhushan in 1968.

Planning and the Second Five-Year Plan

The memoir says that in 1954 the Prime Minister and the Planning Commission asked him to begin planning studies at the Institute. Aiming to double national income and sharply reduce unemployment over twenty years, he produced the two- and four-sector models now associated with his name. Britannica says the Second Five-Year Plan, which ran from 1956 to 1961, encouraged heavy industry and relied on his mathematical description of the economy. The sources differ on when he joined the Planning Commission: the memoir and the Cambridge feature give 1953, Britannica 1955. All three agree he served until 1967.

Statistics Day

Mahalanobis died in Calcutta on 28 June 1972, three weeks after an abdominal operation, and his last rites were held on what would have been his 79th birthday, according to the memoir. The Institute’s annual report records that in 2006, during the Institute’s platinum jubilee, the then Prime Minister declared 29 June National Statistics Day.

The 19th Statistics Day was held at the Dr. Ambedkar International Centre in New Delhi on 29 June 2025, with the theme “75 Years of National Sample Survey”. The ministry’s press release says a commemorative coin and a customised stamp for the survey were released that day. The 75th anniversary programme had opened at Vigyan Bhawan in New Delhi on 7 February 2025, where two Diamond Jubilee publications on the 75 years of the household and enterprise surveys were unveiled.