Decile

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 ${\displaystyle D_{1}}$ to ${\displaystyle D_{9}}$ (${\displaystyle D_{1}}$ = 10th percentile, ${\displaystyle D_{2}}$ = 20th percentile and so on). It is calculated as follows:[3]

${\displaystyle DM={\frac {\sum _{i=1}^{9}D_{i}}{9}}}$

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.