“If this is not what springs immediately to mind as soon as the words “on average” are appended to a description of mean differences, then the words “on average” have not rectified the damage done by the use of means to describe populations of varied individuals.”

Source: The Ape that Kicked the Hornet's Nest (2013), p. 268

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Steve Stewart-Williams63

1971

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“A danger in emphasizing mean values for each sex is that these values may be projected onto all or most normally developing men and women. The mean may be treated as a description of the typical group member, despite the fact that the majority of individuals fall above or below it. Psychologists do make some effort to stress that means cannot be attributed to all members of any group, as evidenced by the fact that we often append the phrase “on average” to our descriptions of mean differences. But is this enough? Consider again the robust sex difference in willingness to engage in casual sex: The mean SO [sociosexuality] score for men is higher than that for women. What does this tell us, though, about individual men and women? It clearly does not tell us that all men are interested in casual sex and that all women are not. However, given the degree of overlap between the male and female distributions, it also does not tell us that a large majority of men are more interested in casual sex than a large majority of women. That is, it is not accurate to say even that “men are typically more interested in casual sex than women, but there are of course exceptions.””

Steve Stewart-Williams (1971)

Here is what the data that the means are drawn from actually tell us:
Men and women can be found at virtually every level of interest in casual sex. At the right-hand tail of the distribution, only a small number of people are strongly interested in casual sex; however, of these people, more are men than women. At the left-hand tail, only a small number of people are strongly <I>dis</I>interested in casual sex; however, of these people, more are women than men. Most people — men <I>and</I> women — fall somewhere in between. If you were to choose one man and one woman at random, it would be somewhat more likely that the man would have higher SO. However, you wouldn't want to bet your life savings on it. Around a third of the time — i.e., closer to 50% than to 0% — the woman would have higher SO.
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Ludwig Wittgenstein book Philosophical Investigations

§ 120
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Witold Doroszewski, Z zagadiiien leksykografii polskiej [Selected Problems of Polish Lexicography], Warszawa 1954, p. 93; as cited in Schaff (1962;6).