Words per minute meaning literally words or characters?

Words. Well, IIRC in tests it's something like an abstract word of fixed length, something like 5 characters or something, as that's the average word length in English. Like, it doesn't mean you're typing "antidisestablishmentarianism" over and over, one word each time.

kagis

Yeah:

https://en.wikipedia.org/wiki/Words_per_minute

Since words vary in length, for the purpose of measurement of text entry the definition of each "word" is often standardized to be five characters or keystrokes long in English,[1] including spaces and punctuation. For example, under such a method applied to plain English text the phrase "I run" counts as one word, but "rhinoceros" and "let's talk" would both count as two.

Karat et al. found in one study of average computer users in 1999 that the average rate for transcription was 32.5 words per minute, and 19.0 words per minute for composition.[2] In the same study, when the group was divided into "fast", "moderate", and "slow" groups, the average speeds were 40 wpm, 35 wpm, and 23 wpm, respectively.

With the onset of the era of desktop computers and smartphones, fast typing skills became much more widespread. As of 2019, the average typing speed on a mobile phone was 36.2 wpm with 2.3% uncorrected errors—there were significant correlations with age, level of English proficiency, and number of fingers used to type.[3] Some typists have sustained speeds over 200 wpm for a 15-second typing test with simple English words.[4]

Typically, professional typists type at speeds of 43 to 80 wpm, while some positions can require 80 to 95 (usually the minimum required for dispatch positions and other time-sensitive typing jobs), and some advanced typists work at speeds above 120 wpm.[5] Two-finger typists, sometimes also referred to as "hunt and peck" typists, commonly reach sustained speeds of about 37 wpm for memorized text and 27 wpm when copying text, but in bursts may be able to reach much higher speeds.[6] From the 1920s through the 1970s, typing speed (along with shorthand speed) was an important secretarial qualification, and typing contests were popular and often publicized by typewriter companies as promotional tools.

Stenotype

Stenotype keyboards enable the trained user to input text as fast as 360 wpm at very high accuracy for an extended period, which is sufficient for real-time activities such as court reporting or closed captioning. While training dropout rates are very high — in some cases only 10% or even fewer graduate — stenotype students are usually able to reach speeds of 100–120 wpm within six months, which is faster than most alphanumeric typists. Guinness World Records gives 360 wpm with 97.23% accuracy as the highest achieved speed using a stenotype.[7]

So it's not a typo or whatever, if that's what you mean.

Because 3 - 4 words per second seems a bit much to me and whoever talks that fast?

It's pretty fast, but then you're talking about a professional text-entry person using the fastest plain-text entry mechanism we know about in a speed test. I'm sure that that's not something demanded of a stenotypist in a normal real-time transcription session.

My guess is that you probably could still make practical use of it if you didn't need real-time transcription by doing a recording and then playing back with software that can do time stretching to accelerate the rate of playback; you could transcribe more-quickly.

'course, automated transcription's getting better too, and that might also be an answer on that front.