The purpose of this paper is to explain usefulness of the mode which appears in a length distribution of fish for separating a mixed group into homogeneous subgroups, e. g., by age.
A mixture of two subgroups each of which distributes normaly with difference of means
d, the ratio of standard deviations Ó and mixing ratio
A are considered. When
d becomes larger than a certain limit
d0, two modes would appear very close to the respective means (Fig. 2). Ratio of the modal values are also near to
A/Ó (Table 1). Sometimes, though
d is less than
d0, existence of heterogeneous group is indicated through a bump in the skirt of the distribution curve. These facts show that the mode can be made use of in isolating a mixed group into subgroups. An effort has been made to obtain the conditions of parameters which enable to separate the mode and have the bump appear (Fig. 3, Fig. 4).
Furthermore, means and areas which were calculated for parts of the distribution curve separated at the point of minimum value, have been compared with the locations of modes and the ratio of modal values, respectively (Table 2, Table 3). As regard to the biases of estimations for the mean values of respective subgroups and the mixing ratio, the modes excel means and areas for the parts. However, it is necessary to discuss the varidity of the mode from the standpoint of sampling error, the problem which should be studied in future.
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