An approximate answer to the right question is better than an exact answer to the wrong question

John Tukey was born in 1915 in New Bedford, Massachusetts. His family recognized his genius at an early age, and after being homeschooled, he attended Brown University, where he earned his bachelor's and master's degrees in chemistry. It was there that he began to develop an interest in abstract mathematics. Continuing his doctoral studies at Princeton University, Tukey completed his PhD in mathematics in 1939. He initially worked on topology, where he made a significant contribution known as the "Tukey lemma." This mathematical theorem has important applications, particularly in the fields of set theory and topology. However, Tukey did not remain in abstract mathematics; under the influence of Samuel S. Wilks, he turned to mathematical statistics and conducted significant work in that field.

During World War II, he worked at the Fire Control Research Office, focusing on issues such as weapon targeting and the evaluation of range-finding devices. These experiences provided him with examples for many of the statistical problems he would investigate in the future and also allowed him to understand the nature of practical problems. Tukey summarized the experience he gained from such practical work with the phrase, "An approximate answer to the right question is better than an exact answer to the wrong question."

In the 1950s, Tukey began working on Andrei Kolmogorov's ideas regarding stochastic processes and developed the "Fast Fourier Transformation" (FFT) method, a computer-based technique for analyzing long sequences of correlations. FFT is an efficient computer algorithm capable of handling large data sets, and it met a great need during the 1950s and 1960s, a time when computers were slower and had smaller memories. Tukey was a pioneer not only in mathematical analysis but also in the development of computer algorithms.

Tukey's interest in computers and his contributions to this field constantly expanded the boundaries of statistical research. My own interest in Tukey's work began while I was pursuing my PhD in statistics and simultaneously working as a research assistant in the computer laboratories of the Statistics and Quantitative Research Center (İSKAR) at Marmara University, which has unfortunately since faded into history. In the 1960s and 1970s, Tukey had pioneered the analysis of large data sets by working alongside engineers and statisticians at Bell Telephone Laboratories. During this period, the capacity of computers to store and analyze large amounts of data began to challenge statistical theory. Tukey worked to make this data meaningful and to develop correct analysis methods. Inspired by these studies, I focused on the subject of "statistical databases" for my thesis and proposed a model for the press sector.

At that time, Tukey revisited the approach of Karl Pearson—whom I will mention in another article—to analyzing the distribution of data and developed a very important series of techniques he called "exploratory data analysis." This approach proposed examining the distribution of data without relying on a predetermined probability model. By giving new names to the characteristics of data distributions, Tukey encouraged his readers to reconsider their assumptions. He also developed graphical tools to examine patterns within data. Some of these tools have become standard in widely used statistical software packages today; for example, "box plots" and "stem-and-leaf plots" are among the most well-known.

Tukey's contributions to the science of statistics were not only theoretical but also related to practical applications. The algorithms and tools he developed for computer programs became the cornerstones of modern statistical analysis. Furthermore, he introduced the terms "bit" (binary digit) and "software" to the scientific world, a fact that few people know.

John Tukey not only contributed to statistical theory through his work but also developed practical solutions for better understanding and correctly interpreting data. His innovative and inquisitive approach deeply influenced the science of statistics, and today we realize that his legacy has become even more prominent as the importance of computers and big data analysis has grown.

Tukey continued to bring new ideas and new approaches to old questions throughout his life, and when he passed away in 2000, the science of statistics had undergone radical changes thanks to his vision. If he were alive today, would he have developed new methods to analyze the content of the billions of posts made by millions of people in what we call social media environments? He most likely would have.