SUMMARY Spherical analogues of the linear and spatial medians are proposed for unimodal, bipolar axial and girdle distributions on the sphere. For unimodal data, the statistical properties of the sample spherical median direction are studied, including comparison with the sample mean direction in the case of Fisher's distribution. Spherical analogues of the one- and k-sample sign test are suggested. The paper parallels the discussion by Brown (1983) for the spatial median.
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N. I. Fisher (1985) studied this question.
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