Distribution of the median, quartiles and interquartile distance in samples from a normal population
成果类型：
Article
署名作者：
Hojo, T
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332422
发表日期：
1931
页码：
315360
关键词：
摘要：
The sampling distribution of the median is nearly normal in all cases; it gives a somewhat less reliable estimate of the population mean than the sample mean does. For very small samples there is little to choose in accuracy between the median and the center (mid-point of range). For large samples the center becomes relatively increasingly unreliable, while the standard error of the median has almost reached its limiting value when n = 20. The standard error of the mean is [image] (where a is the population standard deviation) for any form of population distribution; the ratio to it of the standard errors of the median and center will change with the population form. Further if this be asymmetrical the mean position of median and center in repeated samples no longer lies at the population mean. The distribution of the quartile is_not so closely normal as that of the median, but for n [image] 10 it is probably not far from normal. The standard error of the quartile is somewhat greater than that of the median, tending to a limit of 1.36 [image] as against 1.25 [image]. The distribution of the interquartile distance, Q, is positively skew in small samples, and even for n = 40, but tends to the normal slowly as n increases. The estimate of a from Q is less reliable than that from the sample standard deviation, s; in large samples its standard error tends to be 1.65 X S. E. of s.