Wikipedia:Reference desk/Archives/Mathematics/2016 February 21

= February 21 =

Logical Ambiguity in Expression
Apparently there is a logical ambiguity in "Someone who smokes can’t appreciate this wine.", but I'm currently unable to see it. Thoughts?


 * Belongs on language desk. The ambiguity is that "someone" might refer to one person whose name is unknown or otherwise unstated, or "someone" might be intended to mean "anyone". Loraof (talk) 01:26, 21 February 2016 (UTC)


 * There are two different interpretations of the sentence. The first is "there is at least one person who smokes and can't appreciate this wine"; the second is "any person who smokes can't appreciate this wine". These would be expressed in the predicate calculus in different ways. — Preceding unsigned comment added by 88.105.123.227 (talk) 20:42, 21 February 2016 (UTC)
 * Right, this comes loosely under Interpretation_(logic), and hence is basically the domain of the math desk. Some related info at Ambiguity, see also perhaps vagueness. SemanticMantis (talk) 20:26, 22 February 2016 (UTC)

Correlation
When Pearson's r = 1.0 (perfect correlation), is the covariance always equal to the variance of both data sets? I think so. Also, is the standard deviation of both data sets always equal to the square root of 2? Schyler ( exquirere bonum ipsum ) 20:39, 21 February 2016 (UTC)
 * No and no. — Preceding unsigned comment added by 88.105.123.227 (talk) 20:48, 21 February 2016 (UTC)


 * The formula is covariance = r × [variance(first data set)]1/2 × [variance(second data set)]1/2. If r=1 and the two variances are the same, then the covariance equals that variance. If the variances are different from each other, then the question cannot be interpreted. The variances could be anything, not just 2. Loraof (talk) 23:22, 21 February 2016 (UTC).


 * Anscombe's_quartet_3.svgiance and Pearson_product-moment_correlation_coefficient are our main articles, but also see Anscombe's quartet. SemanticMantis (talk) 20:34, 22 February 2016 (UTC)