19th centuryIntroductionStill to do 

1805  Adrien Marie Legendre publishes the method of least squares in his Nouvelles méthodes pour la détermination des orbites des comètes. According to Stigler (1986, p. 145146) Gauss refers to it as nostrum principium in 1809 and mentions that he already developed the least squares method in 1795, but did not publish it. This causes Legendre to accuse Gauss of plagiarism (see also Eric. W. Weissteins Biography of Gauss. Notice however that Weisstein seems to date Legendres discovery in 1811) 
1809  Carl Friedrich Gauss shows the normal distribution to be a description of how observational errors are distributed in his Theoria Motus Corporum Coelestium in Sectionibus Conicis Solum Ambientum. His line of reasoning however is somewhat circular. 
1810  Pierre Simon Laplace who spots the weakness in Gauss work of 1809, gives a more rigorous and improved version in a supplement to his Mémoire sur les approximations des formules qui sont fonctions de très grand nombres et sur leur application aux probabilités. 
1812  Pierre Simon Laplace publishes his Théorie analytique des probabilités. 
1815  Bessel coins the term probable error (wahrscheinliche Fehler) (Stigler, 1986; p. 242) for the distance between the median and a quartile in a normal distribution (which equals 0.6745 standard deviation). It was the measure for variability until superseded by the standard deviation. 
1835  Adolphe Quetelet presents in Sur l'homme et le developpement de ses facultés, essai d'une physique sociale his ideas on l'homme moyen (the average man); the ideal from whom most of us more or less deviate according to the normal distribution. Quetelet has been mainly important for the way he used statistical methods and ideas already in use in astronomy and mathematics to study human properties and for the way he promoted his approach. 
1837  Somewhat hidden (on page 206) in his Recherchés sur la probabilité des jugements...
Siméon Denis Poisson
presents the distribution, that in 1914 is coined the Poisson distribution by H.E. Soper. Poisson
coins the name 'Law of large numbers'. The Poisson distribution achieves literary status in 1973 when Thomas Pynchon describes the impact distribution of V2 missiles in Gravity's Rainbow 
1867  Pafnuti Chebyshev formulates and proves the inequality . 
1875  Francis Galton introduces the use of quartiles and coins the name ogive for the inverse normal cumulative distribution function. 
1885  Francis Galton uses regression. 
1893  Karl Pearson coins the name standard deviation for the measure of dispersion already (long) known as "root mean square error", "error of mean square" or "mean error" 
1897  Karl Pearson
presents the (Pearson) correlation coefficient. Already in 1888 Galton
toys with the idea but he doesn't pursue this line of thought (Stigler, 1986, p. 297299). The name of Auguste Bravais (1846) is also associated with the correlation coefficient (BravaisPearson Coefficient). But according to Stigler (1986, p. 353) this association is spurious. 