Decile Mean: A New Robust Measure of Central Tendency
Sohel Rana*[a,b] , Md.Siraj-Ud-Doulah[c], Habshah Midi[a,b] and A.H.M. R. Imon[d]* Author for corresponding; e-mail address: srana_stat@yahoo.com
Volume: Vol.39 No.3 (JULY 2012)
Research Article
DOI:
Received: 19 August 2011, Revised: -, Accepted: 9 Febuary 2012, Published: -
Citation: Rana S., Md.siraj-ud-doulah , Midi H. and Imon A.R., Decile Mean: A New Robust Measure of Central Tendency, Chiang Mai Journal of Science, 2012; 39(3): 478-485.
Abstract
In statistics, central tendency of a data set is a measure of the middle or location or typical or expected value of the data set. There are many different descriptive statistics that can be chosen as a measurement of the central tendency and under a well-behaved normal distribution few of them possess some nice and desirable properties. But there is evidence that they may perform poorly in the presence of non-normality or when outliers occur in data. We investigate the performances of some popular and commonly used measures of central tendency such as the mean, the median and the trimmed mean and observe that they may not perform as good as we expect in the presence of non-normality or outliers. In this paper, we proposed a new measure of central tendency which we call Decile Mean (DM) since it is based on deciles. This measure should be fairly robust as it automatically discard extreme observations or outliers from both tails but at the same time is more informative than the median or interquartile mean. The usefulness of the proposed measure is investigated by bootstrap and simulation approach. The results show that decile mean outperforms the mean, the median and the trimmed mean in every respect.