On the mean character and variance of a ranked individual, and the mean variance of the intervals between ranked individuals.
成果类型：
Article
署名作者：
Pearson, K; Pearson, MV
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332423
发表日期：
1931
页码：
364397
关键词：
摘要：
Approximate formulae are obtained for the mean value of any rank in samples of n from any population in which the abscissa can be expressed in powers of the frequency up to the corresponding ordinate. Unfortunately in a normal distribution for very small samples and very extreme ranks the formulae are liable to deviate sensibly from the correct values. For n> 15 the approximation is close. This affords a general solution of Galton''s Problem, that of finding the mean interval between any 2 individuals in a ranked series and the standard error of that interval. The ordinary definition of a quartile when it does not fall on a rank, i.e., half the sum of the adjacent characters, is shown to be unsatisfactory, and a method of improving it is provided. There is no special advantage in the use of the quartile; any pair of mirror ranks in its neighborhood will give a good value for the median, and the quartiles are not the best ranks from which to estimate the standard deviation. One can also determine when the mean is known, the error one is not likely to exceed in supposing the character of the individual in the sth rank to be that of the corresponding individual in the sampled population.