{{Short description|Quantile dividing data into 10 equal parts}} In descriptive statistics, a '''decile''' is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 1/10 of the sample or population.<ref>{{citation|title=Introduction to Statistics and Data Analysis: For the Behavioral Sciences|first=Robert S.|last=Lockhart|publisher=Macmillan|year=1998|isbn=9780716729747|page=78|url=https://books.google.com/books?id=93pxNPtt0coC&pg=PA78}}.</ref> A decile is one possible form of a quantile; others include the quartile and percentile.<ref>{{citation|title=Handbook of Parametric and Nonparametric Statistical Procedures|first=David J.|last=Sheskin|edition=3rd|publisher=CRC Press|year=2003|isbn=9781420036268|page=10|url=https://books.google.com/books?id=bmwhcJqq01cC&pg=PA10}}.</ref> A decile rank arranges the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points.
==Decile mean {{anchor|Mean}}==
A moderately robust measure of central tendency, known as the '''decile mean''', can be computed by making use of a sample's deciles <math>D_{1}</math> to <math>D_{9}</math> (<math>D_{1}</math> = 10th percentile, <math>D_{2}</math> = 20th percentile and so on). It is calculated as follows:<ref name=RanaEtAl2012>{{cite journal | first1 = Sohel | last1 = Rana | first2 = Md. | last2 = Siraj-Ud-Doulah | first3 = Habshah | last3 = Midi | first4 = A. H. M. Rahmatullah | last4 = Imon | title = Decile mean: A new robust measure of central tendency | journal = Chiang Mai Journal of Science | volume = 39 |issue = 3 |pages = 478–485 | date = 2012 | url= https://www.thaiscience.info/journals/Article/CMJS/10905266.pdf }}</ref>
: <math> DM = \frac{\sum_{i=1}^9 D_{i}} {9} </math>
Apart from serving as an alternative for the mean and the truncated mean, it also forms the basis for robust measures of skewness and kurtosis, and even a normality test.<ref name=Siraj-Ud-Doulah2021>{{cite journal | first1 = Md. | last1 = Siraj-Ud-Doulah | title = An Alternative Measures of Moments Skewness Kurtosis and JB Test of Normality | journal = Journal of Statistical Theory and Applications | volume = 20 |issue = 2 |pages = 219–227 | date = 2021 | doi = 10.2991/jsta.d.210525.002 | doi-access = free }}</ref>
==See also== * Summary statistics * Socio-economic decile (for New Zealand schools)
==References== {{reflist}}
Category:Summary statistics
{{statistics-stub}}