On the history of the correction for grouping, 1873-1992 (Q2771547)

The paper is devoted to the history of the ``Sheppard correction'' for sample moments computed by the data grouped by intervals \([t_{j-1},t_j]\), where \(t_j=a+jh\). The first who studied this problem was \textit{T. N. Thiele} [Tidsskr. Mat. 3, 22-31 (1873; JFM 05.0123.02)] but he dealt only with the error term dependent of the anchor point \(a\). This error is negligible for ordinary sample sizes. \textit{W. F. Sheppard} [Proc. Lond. Math. Soc. 29, 353-380 (1898; JFM 29.0191.01)] studied the term dependent on the length of the interval (\(h\)) and found the corrections for the moments (e.g. for the variance \(-h^2/12\)). \textit{H. Bruns} [Wahrscheinlichkeitsrechnung und Kollektivmasslehre. Teubner, Leipzig (1906; JFM 37.0262.02)] and, independently, \textit{R. A. Fisher} [Phil. Trans. R. Soc. London. A 222, 309-368 (1922; JFM 48.1280.02) (note that volume number and pages are wrong in JFM)] investigated both terms.