‘A note on the mean deviation of the binomial distribution.‘

Abstract

Since the publication of this note I have received the following information on earlier work on the subject, of which I was unaware. Prof. O. Reiersel refers to p. 161 of an article by R. Frisch—‘Solution d'un problème du calcul des probabilités’ in Skand. Aktuar. Tidskr . 7 (1924), giving a derivation of formula (2) of my note. Dr L. A. Aroian refers to p. 85 of C. Jordan's Statistique Mathematique (1927) which quotes Frisch's result. Dr E. L. Crow refers to a paper by J. S. Frame—‘Mean deviation of the binomial distribution’, Amer. Math. Mon . 52 (1945), which gives an empirical deduction of formula (2) followed by an approximate formula for the mean deviation, analogous to that implied by my formula (4).