Decile

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.[1] A decile is one possible form of a quantile; others include the quartile and percentile.[2] 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.

Special Usage: The decile mean

A moderately robust measure of central tendency - known as the decile mean - can be computed by making use of a sample's deciles D 1 {\displaystyle D_{1}} to D 9 {\displaystyle D_{9}} ( D 1 {\displaystyle D_{1}} = 10th percentile, D 2 {\displaystyle D_{2}} = 20th percentile and so on). It is calculated as follows:[3]

D M = ∑ i = 1 9 D i 9 {\displaystyle DM={\frac {\sum _{i=1}^{9}D_{i}}{9}}}

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.[4]

See also

  • Summary statistics
  • Socio-economic decile (for New Zealand schools)

References

  1. ^ Lockhart, Robert S. (1998), Introduction to Statistics and Data Analysis: For the Behavioral Sciences, Macmillan, p. 78, ISBN 9780716729747.
  2. ^ Sheskin, David J. (2003), Handbook of Parametric and Nonparametric Statistical Procedures (3rd ed.), CRC Press, p. 10, ISBN 9781420036268.
  3. ^ Rana, Sohel; Siraj-Ud-Doulah, Md.; Midi, Habshah; Imon, A. H. M. Rahmatullah (2012). "Decile mean: A new robust measure of central tendency" (PDF). Chiang Mai Journal of Science. 39 (3): 478–485.
  4. ^ Siraj-Ud-Doulah, Md. (2021). "An Alternative Measures of Moments Skewness Kurtosis and JB Test of Normality". Journal of Statistical Theory and Applications. 20 (2): 219–227. doi:10.2991/jsta.d.210525.002.


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