New Delhi: With the passing of Calyampudi Radhakrishna (CR) Rao, the world of statistics has lost not just a pioneer who helped lay the groundwork for modern statistical analysis, but also the ‘father’ of India’s statistical education system.
CR Rao, who passed away at the age of 102 Tuesday evening, was honoured not only with the Padma Bhushan and Padma Vibhushan—India’s second highest and highest civilian awards—in 1968 and 2001, respectively, but also the 2023 International Prize in Statistics, considered equivalent to the ‘Nobel Prize’ in the field.
“It pains me a lot to inform you that Dr. C. R. Rao passed away this evening (August 22, 2023). He would have attained the age of 103 on September 10th. We have lost not only one of the greatest statisticians but also a great man,” Anil Bera, an Indian-born American econometrist and noted statistician in his own right, posted on X (formerly Twitter).
It pains me a lot to inform you that Dr. C. R. Rao passed away this evening (August 22, 2023). He would have attained the age of 103 on September 10th. We have lost not only one of the Greatest Statisticians but also a Great Man. pic.twitter.com/OXGbJ3Nf4I
— Anil Bera (@AnilBer75410115) August 23, 2023
Rao’s passing has been mourned by politicians and economists alike. For instance, former Rajya Sabha member Subramanian Swamy replied to Bera’s post recalling Rao as a “great scholar and wonderful teacher for students including me in the Indian Statistical Institute, Kolkata”.
Rao’s contributions to statistics encompass a wide spectrum. His seminal research introduced key concepts in statistical analysis that are used and taught even today. He was also instrumental in establishing statistical offices in states and districts across the country, enabling a deeper understanding of India’s economy. Furthermore, he was known for his dedication to mentoring students, many of whom have become prominent figures in the world of statistics in their own right.
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An early aptitude for maths, fostered by mother
CR Rao was born on 10 September 1920, in Huvina Hadagalli, a town in the then Madras Province of (now Karnataka). His father, CD Naidu, was a police inspector, and his mother, A. Laxmikanthamma, was a homemaker. It was she that Rao credited with shaping his lifelong pursuit of knowledge.
“For instilling in me the quest for knowledge, I owe to my mother, A Laxmikanthamma, who, in my younger days, woke me up every day at four in the morning and lit the oil lamp for me to study in the quiet hours of the morning when the mind is fresh,” Rao wrote in a dedication in his book Statistics and Truth: Putting Chance to Work, published in 1989.
Rao’s keen aptitude for mathematics showed itself early on, brought on by a very practical aspect of life—the monetary system in place in India under British rule.
“When Rao was only five years old, in 1925, he was able to memorise multiplication tables up to 16 by 16 (needed for monetary transactions during the British rule),” statistician BLS Prakasa Rao wrote in a 2014 article, titled ‘C.R. Rao: A life in statistics’, in the journal Current Science.
Prakasa Rao explained that the monetary denomination of the Indian rupee at the time was as follows: 16 annas made a rupee, 12 kanis made an anna, and 4 dammidies made a kani.
CR Rao’s early years were marked by flux, given that his father’s job required the family to move every three years or so. But despite this constant churn, Rao’s educational achievements did not miss a beat.
“Rao said that he inherited his father’s analytical ability and his mother’s zeal and industry,” Prakasa Rao noted. “His mother was instrumental in instilling a sense of discipline in him.”
Record-holder from the get-go
Rao completed his BA (Hons) degree in mathematics from Andhra University at the age of 19. During this period, he also spent parts of his extracurricular time solving mathematical problems featured in the journal The Mathematical Student.
He then joined the Indian Statistical Institute in 1941 and received his MA in statistics from Calcutta University in 1943, achieving not just a first-class distinction, but also ranking first in the class. His record of marks remains “unbeaten” even today, according to his profile on the website of the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science (AIMSCS) in Hyderabad.
Notably, Rao was part of the very first batch to complete the MA course in statistics from Calcutta University. This means that his record has stood since the very beginning of the programme.
After his postgraduation, Rao was offered a post as a research scholar at the Indian Statistical Institute (ISI) in 1943 and a part-time job in Calcutta University to teach statistics.
During this time, he continued his independent research, and in 1945 published a seminal paper titled ‘Information and accuracy attainable in the estimation of statistical parameters’. According to the Royal Statistical Society, this paper “broke ground” with research that “had implications beyond the field of statistics and are currently regarded as essential in the analysis of fundamental aspects of physics”.
The 1945 paper led to key areas of research and to new technical terms such as Cramer–Rao inequality and Rao–Blackwellization— concepts that even now appear in undergraduate textbooks on statistics and econometrics.
The next year, he was sent to Cambridge University by PC Mahalanobis, the founder of the ISI and another towering figure in the world of statistics, to aid the university with a problem they had requested help with. While there, he earned his PhD in 1948 for his work on developing new multivariate methodology, another landmark advancement in statistics.
“The 1940s were ungrudgingly CR Rao’s,” noted statistician Terry Speed wrote in the January-February 2010 issue of the IMS Bulletin, a publication of the Institute of Mathematical Statistics. “His 1945 paper, which contains the Cramer-Rao Inequality, Rao-Blackwell Theorem, and the beginning of differential geometry of parameter space will guarantee that, even had he done nothing else—but there was much else.”
Laying foundations for Indian statistical education
Rao returned to India in 1948 and was offered a position as professor at ISI, which he accepted. Over the next several decades, until his retirement at the age of 60, Rao occupied several key posts at ISI and published over 200 research papers. However, his contributions went even further than that.
“As head and later director of the Research and Training School at the ISI for a period of over 40 years, Rao developed research and training programs and produced outstanding students,” says the website of the CR Rao AIMSCS.
“In fact, the courses that led to the B. Stat and M. Stat degrees at ISI today were worked out by Rao,” Prakasa Rao wrote in his profile. “He also initiated the PhD program in theoretical statistics and probability, with D. Basu, who is well-known for his seminal contributions to statistics, being Rao’s first Ph.D. student.”
Both Prakasa Rao and the CR Rao AIMSCS mention in their respective profiles that Rao was just as devoted to his students as he was to his research.
This is perhaps best illustrated by Rao’s own words, when he was asked about his most significant contribution to statistics: “It is the outstanding contributions my students are making to statistical theory and practice.”
But Rao’s contributions to knowledge went beyond academia. Working with Mahalanobis, he was instrumental in the setting up of state statistical bureaus across India and establishing a network of statistical agencies at the district level for data collection — a system that’s still in place.
In his later decades, Rao lived and taught at various universities in the US.
In a video message to viewers during his centenary year celebrations in 2019, Rao spoke about his thoughts on data and its analysis.
“Statistics is the science of learning from data,” he explained. “Today is the age of data revolution. There is, therefore, a heightened need for statistics—both in terms of training in statistics to help analyse and interpret the data, and in terms of research to answer new questions arising from the data… Therefore, we have our work cut out for us as researchers and as teachers. This is the challenge for all of you.”
A timeless lesson and challenge for India and the world.
(Edited by Asavari Singh)
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