**John Wilder Tukey** (/ˈtuːki/; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the Fast Fourier Transform (FFT) algorithm and box plot.^{[2]} The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit' and the first published use of the word software.

## Biography

Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor mother. He was mainly taught by his mother and attended regular classes only for certain subjects like French.^{[3]} Tukey obtained a B.A. in 1936 and M.Sc. in 1937 in chemistry, from Brown University, before moving to Princeton University, where he received a Ph.D. in mathematics after completing a doctoral dissertation titled "On denumerability in topology."^{[4]}^{[5]}

During World War II, Tukey worked at the Fire Control Research Office and collaborated with Samuel Wilks and William Cochran. He is claimed to have helped design the U-2 spy plane. After the war, he returned to Princeton, dividing his time between the university and AT&T Bell Laboratories. In 1962, Tukey was elected to the American Philosophical Society.^{[6]} He became a full professor at 35 and founding chairman of the Princeton statistics department in 1965.^{[3]}

Among many contributions to civil society, Tukey served on a committee of the American Statistical Association that produced a report critiquing the statistical methodology of the Kinsey Report, *Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male*, which summarised "While much remains to be done, our overall impression of their work to date is favorable".

From 1960 to 1980, Tukey helped design the NBC television network polls used to predict and analyze elections. He was also a consultant to the Educational Testing Service, the Xerox Corporation and Merck & Company.

He was awarded the National Medal of Science by President Nixon in 1973.^{[3]} He was awarded the IEEE Medal of Honor in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform (FFT) algorithm".

Tukey retired in 1985. He died in New Brunswick, New Jersey, on July 26, 2000.

## Scientific contributions

Early in his career Tukey worked on developing statistical methods for computers at Bell Labs where he invented the term "bit" in 1947.^{[7]}^{[8]}^{[9]}

His statistical interests were many and varied. He is particularly remembered for his development with James Cooley of the Cooley–Tukey FFT algorithm. In 1970, he contributed significantly to what is today known as the jackknife estimation—also termed Quenouille–Tukey jackknife. He introduced the box plot in his 1977 book, "Exploratory Data Analysis".

Tukey's range test, the Tukey lambda distribution, Tukey's test of additivity, Tukey's lemma, and the Tukey window all bear his name. He is also the creator of several little-known methods such as the trimean and median-median line, an easier alternative to linear regression.

In 1974, he developed, with Jerome H. Friedman, the concept of the projection pursuit.^{[10]}

### Statistical practice

He also contributed to statistical practice and articulated the important distinction between exploratory data analysis and confirmatory data analysis, believing that much statistical methodology placed too great an emphasis on the latter.

Though he believed in the utility of separating the two types of analysis, he pointed out that sometimes, especially in natural science, this was problematic and termed such situations uncomfortable science.

A. D. Gordon offered the following summary of Tukey's principles for statistical practice:^{[citation needed]}

- ... the usefulness and limitation of mathematical statistics; the importance of having methods of statistical analysis that are robust to violations of the assumptions underlying their use; the need to amass experience of the behaviour of specific methods of analysis in order to provide guidance on their use; the importance of allowing the possibility of data's influencing the choice of method by which they are analysed; the need for statisticians to reject the role of "guardian of proven truth", and to resist attempts to provide once-for-all solutions and tidy over-unifications of the subject; the iterative nature of data analysis; implications of the increasing power, availability, and cheapness of computing facilities; the training of statisticians.

## Statistical terms

Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.

While working with John von Neumann on early computer designs, Tukey introduced the word "bit" as a contraction of "binary digit".^{[11]} The term "bit" was first used in an article by Claude Shannon in 1948.

In 2000, Fred Shapiro, a librarian at the Yale Law School, published a letter revealing that Tukey's 1958 paper "The Teaching of Concrete Mathematics"^{[12]}^{[13]} contained the earliest known usage of the term "software" found in a search of JSTOR's electronic archives, predating the OED's citation by two years.^{[14]} This led many to credit Tukey with coining the term, particularly in obituaries published that same year,^{[3]} although Tukey never claimed credit for any such coinage. In 1995, Paul Niquette claimed he had originally coined the term in October 1953, although he could not find any documents supporting his claim.^{[15]} The earliest known publication of the term "software" in an engineering context was in August 1953 by Richard R. Carhart, in a RAND Corporation research memorandum.^{[16]}

## See also

## Publications

- Andrews, David F.; Bickel, Peter J.; Hampel, Frank R.; Huber, Peter J.; Rogers, W. H.; Tukey, John Wilder (1972).
*Robust estimates of location: survey and advances*. Princeton University Press. ISBN 978-0-691-08113-7. OCLC 369963. - Basford, Kaye E.; Tukey, John Wilder (1998).
*Graphical Analysis of Multiresponse Data*. Chapman & Hall/CRC Press. ISBN 978-0-8493-0384-5. OCLC 154674707.^{[17]}^{[18]}^{[19]}^{[20]} - Blackman, R. B.; Tukey, John Wilder (1959).
*The measurement of power spectra from the point of view of communications engineering*. Dover Publications. ISBN 978-0-486-60507-4. - Cochran, William Gemmell; Mosteller, Charles Frederick; Tukey, John Wilder (1953).
*Statistical problems of the Kinsey report on sexual behavior in the human male*. Journal of the American Statistical Association. doi:10.1080/01621459.1953.10501194. - Hoaglin, David C.; Mosteller, Charles Frederick; Tukey, John Wilder, eds. (1983).
*Understanding Robust and Exploratory Data Analysis*. Wiley. ISBN 978-0-471-09777-8. OCLC 8495063. - Hoaglin, David C.; Mosteller, Charles Frederick; Tukey, John Wilder, eds. (1985).
*Exploring Data Tables, Trends and Shapes*. Wiley. ISBN 978-0-471-09776-1. OCLC 11550398. - Hoaglin, David C.; Mosteller, Charles Frederick; Tukey, John Wilder, eds. (1991).
*Fundamentals of exploratory analysis of variance*. Wiley. ISBN 978-0-471-52735-0. OCLC 23180322. - Morgenthaler, Stephan; Tukey, John Wilder, eds. (1991).
*Configural polysampling: a route to practical robustness*. Wiley. ISBN 978-0-471-52372-7. OCLC 22381036. - Mosteller, Charles Frederick; Tukey, John Wilder (1977).
*Data analysis and regression: a second course in statistics*. Addison-Wesley. ISBN 978-0-201-04854-4. OCLC 3235470. - Tukey, John Wilder (1940).
*Convergence and Uniformity in Topology*. Princeton University Press. ISBN 978-0-691-09568-4. OCLC 227948615. - Tukey, John Wilder (1977).
*Exploratory Data Analysis*. Addison-Wesley. ISBN 978-0-201-07616-5. OCLC 3058187. - Tukey, John Wilder; Ross, Ian C.; Bertrand, Verna (1973).
*Index to statistics and probability*. R & D Press. ISBN 978-0-88274-001-0. OCLC 745715.

*The collected works of John W Tukey*, edited by William S. Cleveland

- Brillinger, David R., ed. (1984).
*Volume I: Time series, 1949–1964*. Wadsworth, Inc. ISBN 978-0-534-03303-3. OCLC 10998116. - Brillinger, David R., ed. (1985).
*Volume II: Time series, 1965–1984*. Wadsworth, Inc. ISBN 978-0-534-03304-0. OCLC 159731367. - Jones, Lyle V., ed. (1985).
*Volume III: Philosophy and principles of data analysis, 1949–1964*. Wadsworth & Brooks/Cole. ISBN 978-0-534-03305-7. OCLC 159731367. - Jones, Lyle V., ed. (1986).
*Volume IV: Philosophy and principles of data analysis, 1965–1986*. Wadsworth & Brooks/Cole. ISBN 978-0-534-05101-3. OCLC 165832503. - Cleveland, William S., ed. (1988).
*Volume V: Graphics, 1965–1985*. Wadsworth & Brooks/Cole. ISBN 978-0-534-05102-0. OCLC 230023465. - Mallows, Colin L., ed. (1990).
*Volume VI: More mathematical, 1938–1984*. Wadsworth & Brooks/Cole. ISBN 978-0-534-05103-7. OCLC 232966724. - Cox, David R., ed. (1992).
*Volume VII: Factorial and ANOVA, 1949–1962*. Wadsworth & Brooks/Cole. ISBN 978-0-534-05104-4. OCLC 165366083. - Braun, Henry I., ed. (1994).
*Volume VIII: Multiple comparisons, 1949–1983*. Chapman & Hall/CRC Press. ISBN 978-0-412-05121-0. OCLC 165099761.

- About John Tukey

- O'Connor, John J.; Robertson, Edmund F., "John Tukey",
*MacTutor History of Mathematics archive*, University of St Andrews - Interview of John Tukey about his experience at Princeton

## References

- ^
^{a}^{b}John Tukey at the Mathematics Genealogy Project **^**Sande, Gordon (July 2001). "Obituary: John Wilder Tukey".*Physics Today*.**54**(7): 80–81. doi:10.1063/1.1397408.- ^
^{a}^{b}^{c}^{d}Leonhardt, David (2000-07-28). "John Tukey, 85, Statistician; Coined the Word 'Software'".*New York Times*. Retrieved 2012-09-24. **^**Tukey, John W. (1939).*On denumerability in topology*.**^**"John Tukey".*IEEE Global History Network*. IEEE. Retrieved 2011-07-18.**^**"APS Member History".*search.amphilsoc.org*. Retrieved 2021-01-28.**^**Shannon, Claude Elwood (July 1948). "A Mathematical Theory of Communication" (PDF).*Bell System Technical Journal*.**27**(3): 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x. hdl:11858/00-001M-0000-002C-4314-2. Archived from the original (PDF) on 1998-07-15.The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly

*bits*, a word suggested by J. W. Tukey.**^**Shannon, Claude Elwood (October 1948). "A Mathematical Theory of Communication".*Bell System Technical Journal*.**27**(4): 623–666. doi:10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4314-2.**^**Shannon, Claude Elwood; Weaver, Warren (1949).*A Mathematical Theory of Communication*(PDF). University of Illinois Press. ISBN 0-252-72548-4. Archived from the original (PDF) on 1998-07-15.**^**Friedman, Jerome H.; Tukey, John Wilder (September 1974). "A Projection Pursuit Algorithm for Exploratory Data Analysis".*IEEE Transactions on Computers*.**C-23**(9): 881–890. doi:10.1109/T-C.1974.224051. ISSN 0018-9340. OSTI 1442925. S2CID 7997450.**^**"Bit definition by The Linux Information Project (LINFO)".*www.linfo.org*.**^**Tukey, John Wilder (January 1958). "The Teaching of Concrete Mathematics".*American Mathematical Monthly*. Taylor & Francis, Ltd. / Mathematical Association of America.**65**(1): 1–9, 2. doi:10.2307/2310294. ISSN 0002-9890. JSTOR 2310294. CODEN AMMYAE.[…] Today the "software" comprising the carefully planned interpretive routines, compilers, and other aspects of automative programming are at least as important to the modern electronic calculator as its "hardware" of tubes, transistors, wires, tapes, and the like. […]

**^**Beebe, Nelson H. F. (2017-08-22). "Chapter I - Integer arithmetic".*The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library*(1 ed.). Salt Lake City, UT, USA: Springer International Publishing AG. pp. 969, 1035. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. S2CID 30244721.**^**Shapiro, Fred (2000). "Origin of the Term Software: Evidence from the JSTOR Electronic Journal Archive" (PDF).*IEEE Annals of the History of Computing*.**22**(2): 69–71. doi:10.1109/mahc.2000.887997. Archived from the original (PDF) on 2003-06-05. Retrieved 2013-06-25.**^**Niquette, R. Paul (2006),*Softword: Provenance for the Word 'Software*, ISBN 1-58922-233-4, archived from the original on 2019-08-08, retrieved 2019-08-18**^**Carhart, Richard (1953).*A survey of the current status of the electronic reliability problem*(PDF). Santa Monica, CA: Rand Corporation. p. 69.[…] It will be recalled from Sec. 1.6 that the term

*personnel*was defined to include people who come into direct contact with the hardware, from production to field use, i.e., people who assemble, inspect, pack, ship, handle, install, operate, and maintain electronic equipment. In any of these phases personnel failures may result in unoperational gear. As with the hardware factors, there is almost no quantitative data concerning these software or human factors in reliability: How many faults are caused by personnel, why they occur, and what can be done to remove the errors. […]**^**Talbot, M. (June 2000).*Biometrics*.**56**(2): 649–650. doi:10.1111/j.0006-341X.2000.00647.x. JSTOR 2677019.CS1 maint: untitled periodical (link)**^**Cooper, Mark (July–August 2000).*Crop Science*.**40**(4): 1184. doi:10.2135/cropsci2000.0015br.CS1 maint: untitled periodical (link)**^**Heckler, Charles E. (February 2001).*Technometrics*.**43**(1): 97–98. doi:10.1198/tech.2001.s547. JSTOR 1270862. S2CID 26430218.CS1 maint: untitled periodical (link)**^**Broadfoot, L. (June 2001).*The Journal of Agricultural Science*.**136**(4): 471–475. doi:10.1017/s002185960124893x.CS1 maint: untitled periodical (link)

## External links

Wikiquote has quotations related to: John Tukey |

- Royal Society obit. by Peter McCullagh
- John W. Tukey: His Life and Professional Contributions published in
*The Annals of Statistics* - John Wilder Tukey (1915–2000) in
*Notices of the American Mathematical Society* - Memories of John Tukey
- Short biography by Mary Bittrich
- "John Tukey, 85, Statistician; Coined the Word 'Software'",
*The New York Times*, 2000-07-28 - "Remembering John W. Tukey", special issue of
*Statistical Science* - John Wilder Tukey at the Mathematics Genealogy Project