# Why is it called the “standard” deviation?

I have a simple - and possibly obviously trivial - question: why is the standard deviation called just that, "standard"? Is it because it standardizes the comparison of data sets and results with respect to their dispersion?

A search on Stack Exchange doesn't turn up this question, nor does a Google search on the etymology of the term yield much of value.

• The name "standard deviation" for SD came from Karl Pearson. I would guess no more than that he wanted to recommend it as a standard measure. If anything, I guess that references to standardization either are independent or themselves allude to SD. In principle, many other measures could work as well or better, so there is some arbitrariness in choosing SD. The special role of the SD in the Gaussian is hardly a general argument for using SD. – Nick Cox Oct 4 '15 at 17:39
• An idea, the variance of something is in squares. Say, the variance of the length of a car is 25m2 - this is hard to interpret since we don't normally measure lengths in cubic meters. But taking a square root solves this, we get back to the standard (original) measure, meters. – Repmat Oct 4 '15 at 20:34
• Further to @Nick's comment, the page Earliest Known Uses of Some of the Words of Mathematics says 'The term STANDARD DEVIATION was introduced by Karl Pearson (1857-1936) in 1893, "although the idea was by then nearly a century old" (Abbott; Stigler, page 328). According to the DSB (Dictionary of Scientific Biography): The term "standard deviation" was introduced in a lecture of 31 January 1893, as a convenient substitute for the cumbersome "root mean square error" and the older expressions "error of mean square" and "mean error."' ... – Glen_b -Reinstate Monica Oct 5 '15 at 10:17
• ... "The OED2 shows a use of standard deviation in 1894 by Pearson in "Contributions to the Mathematical Theory of Evolution," (Philosophical Transactions of the Royal Society A, 185, (1894), 71-110.): "Then σ will be termed its standard-deviation (error of mean square)." (p. 80) He had "always found it more convenient to work with the standard-deviation than with the probable error or the modulus, in terms of which the error-function is usually tabulated." (p. 88n) On p. 70 he identified the standard deviation with Gauss’s mean error." – Glen_b -Reinstate Monica Oct 5 '15 at 10:18

Pearson made up this term in 1894 paper "On the dissection of asymmetrical frequency-curves", here's the pdf. Also, he wrote it with a hyphen, "standard-deviation".

He didn't bother to explain us why he chose the term. Gauss and Airy called it mean error (mittlerer Fehler) and error of mean square. In physics it's usually called "dispersion", btw.

My guess is that Pearson used the Gaussian (normal) distribution to motivate the usage, so he probably thought that it's "standard" in that sense.

• Your point about the Gaussian as a "standard" is appealing, and given that there doesn't seem to be more than guesses as to why Pearson coined the term, it really helps with the intuition behind the etymology. Thank you. – Sebastian Hansen Oct 7 '15 at 21:15

I guess that we can have an idea of why a standard deviation is called "standard" by looking at the synonyms of this word (see here). Some of them, like "typical" or "average", make clear the fact that a standard deviation is conceptually a typical or an average deviation to the mean, even if technically speaking you have to take the square root of the averaged squared deviations to the mean of your dataset. In French, we use "écart-type" to refer to standard deviation, "écart" meaning deviation and "type" meaning typical, which probably makes this clearer. I found this a very useful way to provide a conceptual definition of standard deviation to students.

• The grammar checker in a well-known manufacturer's word processor used to flag "standard" as a weak, noninformative word, recommending its deletion, and the word "deviation" as too recherche, recommending it be replaced with something more mainstream, such as "variation" or "variance". In other words, use "variance" in place of "standard deviation". YMMV. – user3697176 Oct 7 '15 at 19:06
• I am not sure to understand your comment. We are talking about the etymological origins of the term "standard deviation". Etymologically speaking, it makes sense to break down the elementary components of compound words to establish their origin. Moreover "variance" is already used to refer to different things (e.g., means of the squared difference between each data point and the mean of the data set), often confusing it with the more general term of "variability". – Psychokwak Oct 8 '15 at 7:22
• I think @user3697176 is just being humorous. – Nick Cox Oct 8 '15 at 8:03
• @user3697176 Did it flag the word recherche as well? – JAB Jan 29 '16 at 14:00