A Person Might Drown While Attempting To Cross a Stream With an Average Depth of Six Inches

W. I. E. Gates? Edward Latham? Bihar Proverb? Washburn Hopkins? R. H. Halsey? Bolton Hall? Anonymous?

Dear Quote Investigator: Statistical averages can be misleading. The maximum and minimum values are not specified when only an average is presented. Here are three versions of a pertinent adage:

(1) A person can drown while crossing a stream with an average depth of six inches.

(2) A six foot tall statistician once drowned in a river with an average depth of only two feet.

(3) An ox drowned in a stream whose average depth was only sufficient to cover the hoof.

This saying has been attributed to W. I. E. Gates, but I have been unable to find a solid citation. Would you please explore this topic?

Quote Investigator: The earliest match located by QI appeared within an 1891 book about proverbs in Bihar, India. The explanation of one proverb referred to a “Kāyath”, a person who worked as clerk, copyist, or calculator. Boldface added to excerpts by QI:^[1]1891, Behar Proverbs: Classified and Arranged by John Christian, Class 3, Proverbs Relating To Peculiarities and Traits, Characteristic of Certain Castes and Classes, Quote Page 119 and 120, Kegan … Continue reading

Once a Kāyath, with his son, was going on a journey. He came to a stream. As he was uncertain of its depth, he proceeded to sound it; and having discovered the depth to be variable, he struck an average. The average depth being what his son could ford, he ordered him, unhesitatingly, to walk through the stream, with the sad consequence that the boy was drowned.

W. I. E. Gates received credit for an instance in 1977, but that was many years after the saying had entered circulation. A detailed citation is given further below.

Here are additional selected citations in chronological order.

In 1899 “Loan Capital: From the Standpoint of Religion and Ethics” by Reverend Edward Latham told a tale about an anonymous Hindu person:^[2]1899, Loan Capital: From the Standpoint of Religion and Ethics by Rev. Edward Latham, Chapter 1: Forbidden Fruit, Quote Page 14, Column 1, Mr. W. J. Squires, London. (Year is based on October 1899 … Continue reading

He is in the position of a certain Hindu who undertook to ford a river. He was 6ft. tall, and the average depth of the river was only 4ft. He was drowned.

In 1900 Major-General Fendall Currie published “Below the Surface”. Currie presented a tragic story from of an anonymous “old man”. A “putwari” is a village registrar or accountant in India:^[3] 1900, Below the Surface by Major-General Fendall Currie, Chapter 8: A Rustic’s Point of View, Quote Page 139, Archibald Constable and Company, Westminster, England. (Google Books Full View) link

“A friend of mine once, about to cross a river, asked the village putwari, whom he met on the bank—a youth educated at the head-quarter’s putwari school—how deep the stream was? The learned youth replied, ‘Oh, there is an average depth of about four feet of water.’ My friend was drowned in trying to wade the stream because the depth was over seven feet in the middle. It is the same with your assessments—all very fair average for good seasons; but there comes a series of bad seasons or a famine, and we are drowned in debt. You are slaves to averages, you English.”

In February 1900 “The Nation” journal of New York printed an article about Hindu proverbs by Washburn Hopkins.^[4]1900 February 1, The Nation, Volume 70, Number 1805, Some Hindu Proverbs by Washburn Hopkins, Start Page 88, Quote Page 89, Column 1, New York Evening Post Company, New York. (Google Books Full View) … Continue reading

A traveller asked a wise man how deep was the river he had to cross. The scholar answered correctly, “The average depth is up to the knee.” So the traveller began to ford the broad stream and in its deep middle was drowned, the sage’s answer remaining as a proverb on the misleading nature of averages.

In 1903 R. H. Halsey, a school president in Wisconsin, delivered a paper at the annual meeting of the National Education Association, and he employed an instance with a doomed ox:^[5]1903, Journal of Proceedings and Addresses of the Forty-Second Annual Meeting of the National Education Association of the U.S., Held at Boston, Massachusetts, July 6-10, 1903, Section: Department of … Continue reading

We have here an illustration of the old Hindoo proverb that “the ox was drowned in the stream whose average depth was only sufficient to cover the hoof.”

In 1904 “Free America: Short Chapters Showing how Liberty Brings Prosperity” by Bolton Hall included the following version of the saying:^[6]1904 Copyright, Free America: Short Chapters Showing how Liberty Brings Prosperity by Bolton Hall, Chapter 5: Who Gets the Wealth You Produce?, Quote Page 48, L. S. Dickey & Company, Chicago, … Continue reading

The man who tried to wade across a stream whose “average” depth was two feet, was drowned.

In 1907 Henry S. Wilcox published “Frailties of the Jury” which contained an instance; the doomed individuals were statisticians:^[7] 1907 Copyright, Frailties of the Jury by Henry S. Wilcox of the Chicago Bar, Chapter 11: Aggregated, Quote Page 94 and 95, Legal Literature Company, Chicago, Illinois. (Google Books Full View) link

’Tis said some statisticians wished to cross a stream and finding out its depth at either side and in its middle from one who knew it well, they ascertained the average was below their stature and thus concluded they could ford the stream. They attempted it and they were drowned. Their figures were correct but not in application to the stream. It had no average depth but was to them as deep as in its deepest part. No quantity of knaves can make an honest man, no sum of fools a sage in wisdom.

The saying continued to be propagated during the ensuing decades. For example, in 1949 a columnist in the “Boston Evening Globe” of Massachusetts wrote the following about pensions:^[8] 1949 September 21, Boston Evening Globe, T. G. M.’s column: The Pensions in Steel and Coal, Quote Page 26, Column 7, Boston, Massachusetts. (Newspapers_com)

They are a difficult, tricky and intricate problem in which figures can lie and words such as “average” play havoc—like the man who was drowned while crossing a stream, the “average” depth of which was only two feet.

In 1961 “LIFE” magazine published a letter from Robert H. Cramer of Woodbury, New Jersey containing the following statement:^[9]1961 December 8, LIFE, Section: Letters To the Editors, Editorial: Phony Statistics, (Letter from Robert H. Cramer of Woodbury, New Jersey), Quote Page 15, Time and LIFE, New York. (Google Books Full … Continue reading

I was reminded of the statistician who sank and drowned while wading a creek with an average depth of three feet.

The saying appeared in a popular 1977 compilation titled “Peter’s Quotations: Ideas for Our Time”:^[10] 1977, Peter’s Quotations: Ideas for Our Time, Compiled by Laurence J. Peter, Section: Statistics, Quote Page 453, William Morrow and Company, New York. (Verified on with hardcopy)

Then there is the man who drowned crossing a stream with an average depth of six inches. —W. I. E. Gates

The same saying appeared in the 1991 compilation “The Wit and Wisdom of Politics”:^[11] 1992, The Wit and Wisdom of Politics, Compiled by Charles Henning, Expanded Edition, Topic: Statistics, Quote Page 249, Fulcrum Publishing, Golden, Colorado. (Verified with scans)

Then there is the man who drowned crossing a stream with an average depth of six inches.
Anonymous

In conclusion, the earliest instance of this didactic saying located by QI appeared in a book of proverbs collected in Bihar, India and published in 1891. The precise origin remains anonymous. The expressions are variegated with different depths mentioned, e.g., four feet, two feet, and six inches. The ill-fated creature is usually a human although an ox succumbs in one version.

Image Notes: Public domain illustration of statistical charts from Wallusy at Pixabay. Image has been cropped.

(Great thanks to Gagandeep S. Datta whose inquiry led QI to formulate this question and perform this exploration.)