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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

observations, Boscovich applied a similar test with respect to absolutedeviations and that Herschel independently (1805) made use **of** it whendetermining the Sun’s movement (again § 6.3.2-3).Herschel (1817/1912, p. 579) wrongly indicated that any starpromiscuously chosen […] out **of** [14,000 stars **of** the first sevenmagnitudes] is not likely to differ much from a certain mean size **of** them all.With regard to size, the stars are incredibly different; that mean value is aworthless quantity, and, in general, stochastic statements, made in theabsence **of** data, are hardly useful. However, it occurred that the stars, evenearlier than the asteroids, had been considered as elements **of** a singlepopulation (in the last-mentioned instance, wrongly).Stellar statistics really originated in the mid-19 th century with the study **of**the proper motions **of** hundreds **of** stars (until 1842, when astronomersstarted to use the Doppler’s invention, only in the directions perpendicularto the appropriate lines **of** sight). The calculated mean proper motions forstars **of** a given magnitude proved, however, almost meaningless sincemagnitudes depended on distances. Beginning with W. Herschel,astronomers thought that the proper motions were random, but theyunderstood randomness in different ways. Newcomb (1902) assumed thattheir projections on an arbitrary axis were normally distributed. He derived,although without providing any calculations, the density laws **of** theirprojections on an arbitrary plane and their own distribution. Both wereconnected with the χ 2 distribution.The general statistical study **of** the starry heaven became more importantthan a precise determination **of** the parameters **of** some star (Hill & Elkin1884, p. 191):The great Cosmical questions to be answered are not so much what is theprecise parallax **of** this or that particular star, but – What are the averageparallaxes **of** those **of** the first, second, third and fourth magnituderespectively, compared with those **of** lesser magnitude? [And] Whatconnection does there subsist between the parallax **of** a star and the amountand direction **of** its proper motion or can it be proved that there is no suchconnection or relation?Then, Kapteyn (1906b; 1909) described a stochastic picture **of** the stellaruniverse by the laws **of** distribution **of** the (random!) parameters, parallaxesand peculiar motions, **of** the stars. He (1906a) also initiated the study **of** thestarry heaven by [stratified] sampling; here is a passage from a letter that hereceived in 1904 on this subject from one **of** his colleagues and inserted onhis p. 67:As in making a contour map, we might take the height **of** points at thecorners **of** squares a hundred meters on a side, but we should also take thetop **of** each hill, the bottom **of** each lake, […], and other distinctive points.In statistics, sampling became recognized at about the same time, althoughnot without serious resistance (You Poh Seng 1951) and its most activepartisan was Kiaer, also see § 10.7-2.The compilation **of** vast numerical materials (catalogues, yearbooks) wasalso **of** a statistical nature. Sometimes this direction **of** work had been104