The relation between the mean difference and the standard deviation in continuous distribution models

Abstract

The objective of the present work is to study the relations between the mean difference and the standard deviation with reference to the most common continuous theoretical distribution models. The continuous distribution models without shape parameters, those with only one shape parameter, and those with two shape parameters have been considered. The shape parameters encountered are inequality indexes, skewness indexes or kurtosis indexes.\ud For the models without shape parameters the perfect equal ranking of the values of the two indexes have been verified. \ud For the models with only one shape parameter it was seen that with variations in the shape parameter both indexes increase or decrease, so that the relation between them is growing. The ratio between the two indexes made it possible to determine the interval in which one index is greater than the other and the one in which it is less. \ud Analogous results emerged for the models with two shape parameters, in particular the region in which one index is greater than the other and the complementary one.\ud It was confirmed that for some models the mean difference has a wider field of definition in terms of the parameters than the standard deviation

Elaboración y análisis de confiabilidad de un cuestionario para medir desde la perspectiva del estudiante, las competencias digitales del docente en entornos no presenciales de enseñanza

“…En la Tabla 3 se pueden observar los resultados a partir del análisis estadístico descriptivo realizado, los cuales se muestran adecuados para cada ítem debido a que no existen desviaciones pronunciadas de la normalidad. Así también, en las desviaciones estándar no se observaron dispersiones altas, lo que indica que no hay presencia de sesgos o valores extremos (Girone, Massari & Manca, 2017). Tabla 3.…”

Mean Difference and Mean Deviation of Tukey Lambda Distribution

“…The purpose of this work is to increase the methodological contributions on the mean difference and on the relationships of the mean difference with other variability indexes [1] [2]. The studies on the mean difference, introduced by Corrado Gini in 1912 as a measure of the variability of the characters according to the aspect of inequality, have aroused the interest of many scholars over years and also recently [3] [4].…”